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 The arxiv list is largely complete.

Preprints

84. Equation of State and Thermometry of the 2D SU($N$) Fermi-Hubbard Model
    G. Pasqualetti, O. Bettermann, N. Darkwah Oppong, E. Ibarra-Garc{\'i}a-Padilla, S. Dasgupta, R. T. Scalettar, K. R. A. Hazzard, I. Bloch, and S. Fölling
    arxiv:2305.18967 (pdf)
    
    Summary

    We characterize the equation of state (EoS) of the SU($N \ge 2$) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N = 3, 4 and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum Monte Carlo (DQMC) and numerical linked cluster expansion (NLCE). By probing the density fluctuations, we compare model-independently temperatures determined by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU(N) FHM.
    Bibtex

    @Article{pasqualetti:equation_2023, author = { G. Pasqualetti, O. Bettermann, N. Darkwah Oppong, E. Ibarra-García-Padilla, S. Dasgupta, R. T. Scalettar, K. R. A. Hazzard, I. Bloch, and S. F{\"o}lling }, title = { Equation of State and Thermometry of the 2D SU($N$) Fermi-Hubbard Model }, journal = { arxiv:2305.18967 }}
83. Classical Analog of Quantum Models in Synthetic Dimensions
    M. Cohen, M. Casebolt, Y. Zhang, K. R. A. Hazzard, and R. Scalettar
    arxiv:2212.07017 (pdf)
    
    Summary

    We introduce a classical analog of quantum matter in ultracold molecule- or Rydberg atom-synthetic dimensions, extending the Potts model to include interactions $J_1$ between atoms adjacent in both real and synthetic space and studying its finite temperature properties. For intermediate values of $J_1$, the resulting phases and phase diagrams are similar to those of the clock and Villain models, in which three phases emerge. There exists a sheet phase analogous to that found in quantum synthetic dimension models between the high temperature disordered phase and the low temperature ferromagnetic phase. We also employ machine learning to uncover non-trivial features of the phase diagram using the learning by confusion approach.
    Bibtex

    @Article{cohen:classical_2022, author = { M. Cohen and M. Casebolt and Y. Zhang and K. R. A. Hazzard and and R. Scalettar }, title = { Classical Analog of Quantum Models in Synthetic Dimensions }, journal = { arXiv:2212.07017}}
82. Motional decoherence in ultracold Rydberg atom quantum simulators of spin models
    Zewen Zhang, Ming Yuan, Bhuvanesh Sundar, and Kaden R. A. Hazzard
    arXiv:2201.08463 (pdf)
    
    Summary

    Ultracold Rydberg atom arrays are an emerging platform for quantum simulation and computing. However, decoherence in these systems remains incompletely understood. Recent experiments [Guardado-Sanchez et al. Phys. Rev. X 8, 021069 (2018)] observed strong decoherence in the quench and longitudinal-field-sweep dynamics of two-dimensional Ising models realized with Lithium-6 Rydberg atoms in optical lattices. This decoherence was conjectured to arise from spin-motion coupling. Here we show that spin-motion coupling indeed leads to decoherence in qualitative, and often quantitative, agreement with the experimental data, treating the difficult spin-motion coupled problem using the discrete truncated Wigner approximation method. We also show that this decoherence will be an important factor to account for in future experiments with Rydberg atoms in optical lattices and microtrap arrays, and discuss methods to mitigate the effect of motion, such as using heavier atoms or deeper traps.
    Bibtex

    @Article{zhang:motional_2022, author = {Zewen Zhang and Ming Yuan and Bhuvanesh Sundar and Kaden R. A. Hazzard}, title = { Motional decoherence in ultracold Rydberg atom quantum simulators of spin models}, journal = { arXiv:2201.08463 }}
81. A quantum algorithm to count weighted ground states of classical spin Hamiltonians
    Bhuvanesh Sundar, Roger Paredes, David T. Damanik, Leonardo Dueñas-Osorio, and Kaden R. A. Hazzard
    arxiv:1908.01745 (pdf)
    
    Summary

    Ground state counting plays an important role in several applications in science and engineering, from estimating residual entropy in physical systems, to bounding engineering reliability and solving combinatorial counting problems. While quantum algorithms such as adiabatic quantum optimization (AQO) and quantum approximate optimization (QAOA) can minimize Hamiltonians, they are inadequate for counting ground states. We modify AQO and QAOA to count the ground states of arbitrary classical spin Hamiltonians, including counting ground states with arbitrary nonnegative weights attached to them. As a concrete example, we show how our method can be used to count the weighted fraction of edge covers on graphs, with user-specified confidence on the relative error of the weighted count, in the asymptotic limit of large graphs. We find the asymptotic computational time complexity of our algorithms, via analytical predictions for AQO and numerical calculations for QAOA, and compare with the classical optimal Monte Carlo algorithm (OMCS), as well as a modified Grover's algorithm. We show that for large problem instances with small weights on the ground states, AQO does not have a quantum speedup over OMCS for a fixed error and confidence, but QAOA has a sub-quadratic speedup on a broad class of numerically simulated problems. Our work is an important step in approaching general ground-state counting problems beyond those that can be solved with Grover's algorithm. It offers algorithms that can employ noisy intermediate-scale quantum devices for solving ground state counting problems on small instances, which can help in identifying more problem classes with quantum speedups.
    Bibtex

    @Article{sundar:quantum_2019, author = {B. Sundar and R. Paredes and D. T. Damanik and L. Due{\~n}as-Osorio and Kaden R. A. Hazzard }, title = { A quantum algorithm to count weighted ground states of classical spin Hamiltonians }, journal = { arxiv:1908.01745 }}
80. Quantum dynamics from a numerical linked cluster expansion
    Ian G. White, Bhuvanesh Sundar, and Kaden R. A. Hazzard
    arxiv:1710.07696 (pdf)
    
    Summary

    We demonstrate that a numerical linked cluster expansion method is a powerful tool to calculate quantum dynamics. We calculate the dynamics of the magnetization and spin correlations in the two-dimensional transverse field Ising and XXZ models evolved from a product state. Such dynamics are directly probed in ongoing experiments in ultracold atoms, molecules, and ions. We show that a numerical linked cluster expansion gives dramatically more accurate results at short-to-moderate times than exact diagonalization, and simultaneously requires fewer computational resources. More specifically, the cluster expansion frequently produces more accurate results than an exact diagonalization calculation that would require $10^5$-- $10^{10}$ more computational operations and memory.
    Bibtex

    @Article{white:quantum_2017, author = {Ian G. White and Bhuvanesh Sundar and Kaden R. A. Hazzard}, title = {Quantum dynamics from a numerical linked cluster expansion}, journal = {arxiv:1710.07696} }

Journal publications

79. Locality of gapped ground states in systems with power-law decaying interactions
    Zhiyuan Wang and Kaden R. A. Hazzard
    PRX Quantum (accepted) (arxiv:2208.13057, pdf)
    
    Summary

    It has been proved that in gapped ground states of locally-interacting lattice quantum systems with a finite local Hilbert space, the effect of local perturbations decays exponentially with distance. However, in systems with power-law~(1/r^α) decaying interactions, no analogous statement has been shown, and there are serious mathematical obstacles to proving it with existing methods. In this paper we prove that when α exceeds the spatial dimension D, the effect of local perturbations on local properties a distance r away is upper bounded by a power law 1/r^α_1 in gapped ground states, provided that the perturbations do not close the spectral gap. The power-law exponent α_1 is tight if α greaterthan 2D and interactions are two-body, where we have α_1=α. The proof is enabled by a method that avoids the use of quasiadiabatic continuation and incorporates techniques of complex analysis. This method also improves bounds on ground state correlation decay, even in short-range interacting systems. Our work generalizes the fundamental notion that local perturbations have local effects to power-law interacting systems, with broad implications for numerical simulations and experiments.
    Bibtex

    @Article{wang:locality_2022, author = { Zhiyuan Wang and Kaden R. A. Hazzard }, title = { Locality of gapped ground states in systems with power-law decaying interactions }, journal = { PRX Quantum (accepted), arXiv:2208.13057}}
78. Quick Study: Synthetic Dimensions
    Kaden R. A. Hazzard and Bryce Gadway
    Physics Today 76(4), 62 (2023) (pdf)
    
    Summary

    Novel geometries can be created using microwaves to couple the internal states of atoms or molecules and mimic movement in real space.
    Bibtex

    @Article{hazzard:synthetic_2023, author = {Hazzard,Kaden R. A. and Gadway,Bryce }, title = {Synthetic dimensions}, journal = {Physics Today}, volume = {76}, number = {4}, pages = {62-63}, year = {2023}, doi = {10.1063/PT.3.5225} }
77. Topological correlations in three dimensional classical Ising models: an exact solution with a continuous phase transition
    Zhiyuan Wang and Kaden R. A. Hazzard
    Phys. Rev. Research 5, 013086 (2023) (arxiv:2202.11303, pdf)
    
    Summary

    We study a three-dimensional (3D) classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. The solution combines and generalizes the Onsager-Kaufman solution [L. Onsager, Phys. Rev. 65, 117 (1944); B. Kaufman, Phys. Rev. 76, 1232 (1949)] of the 2D Ising model and the solution of Kitaev's honeycomb model [A. Kitaev, Ann. Phys, 321, 2 (2006)], leading to a three-parameter phase diagram with a third-order phase transition between two distinct phases. Interestingly, the phases of this model are distinguished by topological features: the expectation value of a certain family of loop observables depend only on the topology of the loop (whether the loop is contractible), and are quantized at rational values that differ in the two phases. We show that a related exactly solvable 3D classical statistical model with real coupling constants also shows the topological features of one of these phases. Furthermore, even in the model with complex parameters, the partition function has some physical relevance, as it can be interpreted as the transition amplitude of a quantum dynamical process and may shed light on dynamical quantum phase transitions.
    Bibtex

    @Article{wang:topological_2022, title = {Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition}, author = {Wang, Zhiyuan and Hazzard, Kaden R. A.}, journal = {Phys. Rev. Res.}, volume = {5}, issue = {1}, pages = {013086}, numpages = {18}, year = {2023}, month = {Feb}, publisher = {American Physical Society}, doi = {10.1103/PhysRevResearch.5.013086}, url = {https://link.aps.org/doi/10.1103/PhysRevResearch.5.013086} }
76. Multi-round QAOA and advanced mixers on a trapped-ion quantum computer
    Yingyue Zhu, Zewen Zhang, Bhuvanesh Sundar, Alaina M. Green, C. Huerta Alderete, Nhung H. Nguyen, Kaden R. A. Hazzard, and Norbert M. Linke
    Quantum Sci. Technol. 8, 015007 (2023) (arxiv:2201.12335, pdf)
    
    Summary

    Combinatorial optimization problems on graphs have broad applications in science and engineering. The quantum approximate optimization algorithm (QAOA) is a method to solve these problems on a quantum computer by applying multiple rounds of variational circuits. However, there exist several challenges limiting the application of QAOA to real-world problems. In this paper, we demonstrate on a trapped-ion quantum computer that QAOA results improve with the number of rounds for multiple problems on several arbitrary graphs. We also demonstrate an advanced mixing Hamiltonian that allows sampling of all optimal solutions with predetermined weights. Our results are a step toward applying quantum algorithms to real-world problems.
    Bibtex

    @article{zhu:multi-round_2023, doi = {10.1088/2058-9565/ac91ef}, url = {https://dx.doi.org/10.1088/2058-9565/ac91ef}, year = {2022}, month = {nov}, publisher = {IOP Publishing}, volume = {8}, number = {1}, pages = {015007}, author = {Yingyue Zhu and Zewen Zhang and Bhuvanesh Sundar and Alaina M Green and C Huerta Alderete and Nhung H Nguyen and Kaden R A Hazzard and Norbert M Linke}, title = {Multi-round QAOA and advanced mixers on a trapped-ion quantum computer}, journal = {Quantum Science and Technology} }
75. A two-dimensional programmable tweezer array of fermions
    Zoe Z. Yan, Benjamin M. Spar, Max L. Prichard, Sungjae Chi, Hao-Tian Wei, Eduardo Ibarra-García-Padilla, Kaden R. A. Hazzard, and Waseem S. Bakr
    Phys. Rev. Lett. 129, 123201 (2022) [Editor's Suggestion] (arxiv:2203.15023, pdf)
    
    In the News
    "Strobing Light Shapes Atomic Array", Synopsis appearing in Physics 15, s120 (2022)
    Summary

    We prepare high-filling two-component arrays of tens of fermionic 6 Li atoms in optical tweezers, with the atoms in the ground motional state of each tweezer. Using a stroboscopic technique, we configure the arrays in various two-dimensional geometries with negligible Floquet heating. A full spin- and density-resolved readout of individual sites allows us to postselect near-zero entropy initial states for fermionic quantum simulation. We prepare a correlated state in a two-by-two tunnel-coupled Hubbard plaquette, demonstrating all the building blocks for realizing a programmable fermionic quantum simulator.
    Bibtex

    @article{yan:two-dimensional_2022, title = {Two-Dimensional Programmable Tweezer Arrays of Fermions}, author = {Yan, Zoe Z. and Spar, Benjamin M. and Prichard, Max L. and Chi, Sungjae and Wei, Hao-Tian and Ibarra-Garc\'{\i}a-Padilla, Eduardo and Hazzard, Kaden R. A. and Bakr, Waseem S.}, journal = {Phys. Rev. Lett.}, volume = {129}, issue = {12}, pages = {123201}, numpages = {6}, year = {2022}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.129.123201}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.129.123201} }
74. Observation of antiferromagnetic correlations in an ultracold SU(N) Hubbard model
    Shintaro Taie, Eduardo Ibarra-García-Padilla, Naoki Nishizawa, Yosuke Takasu, Yoshihito Kuno, Hao-Tian Wei, Richard T. Scalettar, Kaden R. A. Hazzard, and Yoshiro Takahashi
    Nature Physics 18, 1356 (2022) (arxiv:2010.07730, pdf)
    
    In the News
    "A cool quantum simulator", Nature Physics News and Views
    "Quantum magnet is billions of times colder than interstellar space", New Scientist
    "Scientists used lasers to make the coldest matter in the universe", Popular Science
    "Scientists create coldest matter in the universe in a lab", space.com
    "Physicists cool particles to less than a billionth of a degree above absolute zero to probe quantum magnetism", Cosmos Magazine
    "SU(N) matter is about 3 billion times colder than deep space", Rice News
    [also on reddit (r/science r/physics #1, r/physics #2, r/space), ScienceToday youtube channel, Ciência News youtube channel, phys.org, Principia Physics, UC Davis News, ...]
    Summary

    Mott insulators are paradigmatic examples of strongly correlated physics from which many phases of quantum matter with hard-to-explain properties emerge. Extending the typical SU(2) spin symmetry of Mott insulators to SU(N) is predicted to produce exotic quantum magnetism at low temperatures. In this work, we experimentally observe nearest-neighbour spin correlations in a SU(6) Hubbard model realized by ytterbium atoms in optical lattices. We study one-dimensional, two-dimensional square and three-dimensional cubic lattice geometries. The measured SU(6) spin correlations are enhanced compared with the SU(2) correlations, owing to strong Pomeranchuk cooling. The experimental data for a one-dimensional lattice agree qualitatively with our theoretical calculations, with an error of at most 30%, without any fitting parameters. Detailed comparison between theory and experiment allows us to infer the temperature to be the lowest achieved for a cold-atom Fermi-Hubbard model. For three-dimensional lattices, the experiments reach entropies below the regime where our calculations converge, highlighting the importance of these experiments as quantum simulations.
    Bibtex

    @Article{taie:observation_2020, author = {Taie, Shintaro and Ibarra-García-Padilla, Eduardo and Nishizawa, Naoki and Takasu, Yosuke and Kuno, Yoshihito and Wei, Hao-Tian and Scalettar, Richard T. and Hazzard, Kaden R. A. and Takahashi, Yoshiro}, title = {Observation of antiferromagnetic correlations in an ultracold SU(N) Hubbard model}, pages = {1356--1361}, volume = {18}, journal = {Nature Physics}, refid = {Taie2022}, year = {2022}, }
73. Quantum Membrane Phases in Synthetic Lattices of Cold Molecules or Rydberg Atoms
    Chunhan Feng, Hannah Manetsch, Valery G. Rousseau, Kaden R. A. Hazzard, and Richard Scalettar
    Phys. Rev. A 105, 063320 (2022) (arxiv:2202.08540, pdf)
    
    Summary

    We calculate properties of dipolar interacting ultracold molecules or Rydberg atoms in a semisynthetic three-dimensional configuration—one synthetic dimension plus a two-dimensional real-space optical lattice or periodic microtrap array—using the stochastic Green's function quantum Monte Carlo method. Through a calculation of thermodynamic quantities and appropriate correlation functions, along with their finite-size scalings, we show that there is a second-order transition to a low-temperature phase in which two-dimensional “sheets” form in the synthetic dimension of internal rotational or electronic states of the molecules or Rydberg atoms, respectively. Simulations for different values of the interaction $V$, which acts between atoms or molecules that are adjacent both in real and synthetic space, allow us to compute a phase diagram. We find a finite-temperature transition at sufficiently large $V$ as well as a quantum phase transition—a critical value $V_c$ below which the transition temperature vanishes.
    Bibtex

    @Article{feng:quantum_2022, title = {Quantum membrane phases in synthetic lattices of cold molecules or Rydberg atoms}, author = {Feng, Chunhan and Manetsch, Hannah and Rousseau, Valery G. and Hazzard, Kaden R. A. and Scalettar, Richard}, journal = {Phys. Rev. A}, volume = {105}, issue = {6}, pages = {063320}, numpages = {8}, year = {2022}, month = {Jun}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.105.063320}, url = {https://link.aps.org/doi/10.1103/PhysRevA.105.063320} } }
72. A tensor network discriminator architecture for classification of quantum data on
    quantum computers
    Michael L. Wall, Paraj Titum, Gregory Quiroz, Michael Foss-Feig, and Kaden R. A. Hazzard
    Phys. Rev. A 105, 062439 (2022) (arxiv:2202.10911, pdf)
    
    Summary

    We demonstrate the use of matrix product state (MPS) models for discriminating quantum data on quantum computers using holographic algorithms, focusing on the problem of classifying a translationally invariant quantum state based on $L$ qubits of quantum data extracted from it. We detail a process in which data from single-shot experimental measurements are used to optimize an isometric tensor network, the isometric tensors are compiled into unitary quantum operations using greedy compilation heuristics, parameter optimization on the resulting quantum circuit model removes the postselection requirements of the isometric tensor model, and the resulting quantum model is inferenced on either product state (single-shot measurement) or entangled quantum data. We demonstrate our training and inference architecture on a synthetic dataset of six-site single-shot measurements from the bulk of a one-dimensional transverse field Ising model (TFIM) deep in its antiferromagnetic and paramagnetic phases. We find that increasing the bond dimension of the tensor-network model, amounting to adding more ancilla qubits to the circuit representation, improves both the average number of correct classifications across the dataset and the single-shot probability of correct classification. We experimentally evaluate models on Quantinuum's H1-2 trapped ion quantum computer using entangled input data modeled as translationally invariant, bond dimension 4 MPSs across the known quantum phase transition of the TFIM. Using linear regression on the experimental data near the transition point, we find predictions for the critical transverse field of $h=0.962$ and 0.994 for tensor-network discriminators of bond dimension χ = 2 and χ=4, respectively. These predictions compare favorably with the known transition location of h=1 despite training on data far from the transition point. Our techniques identify families of short-depth variational quantum circuits in a data-driven and hardware-aware fashion and robust classical techniques to precondition the model parameters, and can be adapted beyond machine learning to myriad applications of tensor networks on quantum computers, such as quantum simulation and error correction.
    Bibtex

    @Article{wall:tensor_2022, title = {Tensor-network discriminator architecture for classification of quantum data on quantum computers}, author = {Wall, Michael L. and Titum, Paraj and Quiroz, Gregory and Foss-Feig, Michael and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {105}, issue = {6}, pages = {062439}, numpages = {17}, year = {2022}, month = {Jun}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.105.062439}, url = {https://link.aps.org/doi/10.1103/PhysRevA.105.062439} }
71. Realizing Su-Schrieffer-Heeger topological edge states in Rydberg-atom synthetic dimensions
    S. K. Kanungo, J. D. Whalen, Y. Lu, M. Yuan, S. Dasgupta, F. B. Dunning, K. R. A. Hazzard, and T. C. Killian
    Nature Communications 13, 972 (2022) (arxiv:2101.02871, pdf)
    
    In the News
    "Physicists harness electrons to make `synthetic dimensions'", Rice University News
    (also on phys.org, ScienceDaily, SciTechDaily, ...)
    Summary

    A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold 84Sr atom, we demonstrate a synthetic-dimension based on Rydberg levels coupled with millimeter waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian, a paradigmatic model of topological matter. Band structure is probed through optical excitation from the ground state to Rydberg levels, revealing symmetry-protected topological edge states at zero energy. Edge-state energies are robust to perturbations of tunneling-rates that preserve chiral symmetry, but can be shifted by the introduction of on-site potentials.
    Bibtex

    @Article{kanungo:realizing_2021, author = {Kanungo, S. K. and Whalen, J. D. and Lu, Y. and Yuan, M. and Dasgupta, S. and Dunning, F. B. and Hazzard, K. R. A. and Killian, T. C.}, title = {Realizing topological edge states with Rydberg-atom synthetic dimensions}, issn = {2041-1723}, number = {1}, pages = {972}, url = {https://doi.org/10.1038/s41467-022-28550-y}, volume = {13}, abstract = {A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold 84Sr atom, we demonstrate a synthetic-dimension based on Rydberg levels coupled with millimeter waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian, a paradigmatic model of topological matter. Band structure is probed through optical excitation from the ground state to Rydberg levels, revealing symmetry-protected topological edge states at zero energy. Edge-state energies are robust to perturbations of tunneling-rates that preserve chiral symmetry, but can be shifted by the introduction of on-site potentials.}, journal = {Nature Communications}, refid = {Kanungo2022}, year = {2022}, }
70. Complex collisions of ultracold molecules: a toy model
    Jia K. Yao, Cooper A. Johnson, Nirav P. Mehta, and Kaden R. A. Hazzard
    Phys. Rev. A 104, 053311 (2021) (arxiv:1906.06960, pdf)
    
    Summary

    We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system and argue that it offers lessons for real molecular collisions in three dimensions. We analyze the distribution of the adiabatic potentials in the hyperspherical coordinate representation as well as the distribution of near-threshold four-body bound states, systematically studying the effects of molecular properties, such as interaction strength, interaction range, and atomic mass. It is found that the adiabatic potential's nearest-neighbor energy level distribution transitions from significant level repulsion characteristic of chaos (Brody distribution) to nonchaotic (Poisson distribution) as the two molecules are separated. For the near-threshold four-atom bound states, the case where all atoms have equal masses shows a Poissonian spacing distribution, while the unequal-mass system exhibits significant level repulsion characterized by a nonzero Brody parameter. We derive a semiclassical formula for the density of states and extract from it simple scaling laws with potential depth and range. We find good agreement between the semiclassical predictions for the density of states and the full quantum mechanical calculations.
    Bibtex

    @article{yao:complex_2021, title = {Complex collisions of ultracold molecules: A toy model}, author = {Yao, Jia K. and Johnson, Cooper A. and Mehta, Nirav P. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {104}, issue = {5}, pages = {053311}, numpages = {14}, year = {2021}, month = {Nov}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.104.053311}, url = {https://link.aps.org/doi/10.1103/PhysRevA.104.053311} }
69. Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
    Eduardo Ibarra-García-Padilla, Sohail Dasgupta, Hao-Tian Wei, Shintaro Taie, Yoshiro Takahashi, Richard T. Scalettar, and Kaden R. A. Hazzard
    Phys. Rev. A 104, 043316 (2021) [Editor's Suggestion] (arxiv:2108.04153, pdf)
    
    Summary

    The SU(2) symmetric Fermi-Hubbard model (FHM) plays an essential role in strongly correlated fermionic many-body systems. In the one particle per site and strongly interacting limit U/t≫1, it is effectively described by the Heisenberg Hamiltonian. In this limit, enlarging the spin and extending the typical SU(2) symmetry to SU(N) has been predicted to give exotic phases of matter in the ground state, with a complicated dependence on N. This raises the question of what—if any—are the finite-temperature signatures of these phases, especially in the currently experimentally relevant regime near or above the superexchange energy. We explore this question for thermodynamic observables by numerically calculating the thermodynamics of the SU(N) FHM in the two-dimensional square lattice near densities of one particle per site, using determinant quantum Monte Carlo and numerical linked cluster expansion. Interestingly, we find that for temperatures above the superexchange energy, where the correlation length is short, the energy, number of on-site pairs, and kinetic energy are universal functions of N. Although the physics in the regime studied is well beyond what can be captured by low-order high-temperature series, we show that an analytic description of the scaling is possible in terms of only one- and two-site calculations.
    Bibtex

    @Article{ibarra-garcia-padilla:universal_2021, title = {Universal thermodynamics of an $\mathrm{SU}(N)$ Fermi-Hubbard model}, author = {Ibarra-Garc\'{\i}a-Padilla, Eduardo and Dasgupta, Sohail and Wei, Hao-Tian and Taie, Shintaro and Takahashi, Yoshiro and Scalettar, Richard T. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {104}, issue = {4}, pages = {043316}, numpages = {20}, year = {2021}, month = {Oct}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.104.043316}, url = {https://link.aps.org/doi/10.1103/PhysRevA.104.043316} }
68. Viewpoint: Photons Get Slippery
    Kaden R. A. Hazzard
    Physics 14, 139 (2021) (pdf)
    
    Summary

    Researchers have turned light into a superfluid by using a “synthetic” dimension, which is created by using temporal degrees of freedom to mimic spatial degrees of freedom.
    Bibtex

    @article{hazzard:viewpoint-photons_2021, title = {Photons Get Slippery}, author = {Hazzard, Kaden R. A.}, journal = {Physics}, volume = {14}, pages = {139}, year = {2021} }
67. Nonlinear Dynamics in a Synthetic Momentum-State Lattice
    F. A. An, B. Sundar, J. Hou, X.-W. Luo, E. J. Meier, C. Zhang, Kaden R. A. Hazzard, and B. Gadway
    Phys. Rev. Lett. 127, 130401 (2021) [Editor's Suggestion] (arxiv:2105.04429, pdf)
    
    Summary

    The scope of analog simulation in atomic, molecular, and optical systems has expanded greatly over the past decades. Recently, the idea of synthetic dimensions—in which transport occurs in a space spanned by internal or motional states coupled by field-driven transitions—has played a key role in this expansion. While approaches based on synthetic dimensions have led to rapid advances in single-particle Hamiltonian engineering, strong interaction effects have been conspicuously absent from most synthetic dimensions platforms. Here, in a lattice of coupled atomic momentum states, we show that atomic interactions result in large and qualitative changes to dynamics in the synthetic dimension. We explore how the interplay of nonlinear interactions and coherent tunneling enriches the dynamics of a one-band tight-binding model giving rise to macroscopic self-trapping and phase-driven Josephson dynamics with a nonsinusoidal current-phase relationship, which can be viewed as stemming from a nonlinear band structure arising from interactions.
    Bibtex

    @article{an:nonlinear_2021, title = {Nonlinear Dynamics in a Synthetic Momentum-State Lattice}, author = {An, Fangzhao Alex and Sundar, Bhuvanesh and Hou, Junpeng and Luo, Xi-Wang and Meier, Eric J. and Zhang, Chuanwei and Hazzard, Kaden R. A. and Gadway, Bryce}, journal = {Phys. Rev. Lett.}, volume = {127}, issue = {13}, pages = {130401}, numpages = {7}, year = {2021}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.127.130401}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.127.130401} }
66. Bounding the finite-size error of quantum many-body dynamics simulations
    Zhiyuan Wang, Michael Foss-Feig, Kaden R. A. Hazzard
    Phys. Rev. Research 3, L032047 (2021) (arxiv:2009.12032, pdf)
    
    Summary

    Finite-size errors (FSEs), the discrepancies between an observable in a finite system and in the thermodynamic limit, are ubiquitous in numerical simulations of quantum many-body systems. Although a rough estimate of these errors can be obtained from a sequence of finite-size results, a strict, quantitative bound on the magnitude of FSE is still missing. Here we derive rigorous upper bounds on the FSE of local observables in real-time quantum dynamics simulations initialized from a product state. In d-dimensional locally interacting systems with a finite local Hilbert space, our bound implies ∣∣⟨S(t)⟩L−⟨S(t)⟩_{\infty}|≤C(2vt/L)cL−μ, with v, C, c, μ constants independent of L and t, which we compute explicitly. For periodic boundary conditions (PBCs), the constant c is twice as large as that for open boundary conditions (OBCs), suggesting that PBCs have smaller FSEs than OBCs at early times. The bound can be generalized to a large class of correlated initial states as well. As a byproduct, we prove that the FSE of local observables in ground-state simulations decays exponentially with L under a suitable spectral gap condition. Our bounds are practically useful in determining the validity of finite-size results, as we demonstrate in simulations of the one-dimensional (1D) quantum Ising and Fermi-Hubbard models.
    Bibtex

    @article{wang:bounding_2021, title = {Bounding the finite-size error of quantum many-body dynamics simulations}, author = {Wang, Zhiyuan and Foss-Feig, Michael and Hazzard, Kaden R. A.}, journal = {Phys. Rev. Research}, volume = {3}, issue = {3}, pages = {L032047}, numpages = {8}, year = {2021}, month = {Aug}, publisher = {American Physical Society}, doi = {10.1103/PhysRevResearch.3.L032047}, url = {https://link.aps.org/doi/10.1103/PhysRevResearch.3.L032047} }
65. Quantum simulators: architectures and opportunities
    E. Altman et al. (Kaden R. A. Hazzard and 36 others)
    PRX Quantum 2, 017003 (2021) (arxiv:1912.06938, pdf)
    
    Summary

    Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behavior to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the National Science Foundation workshop on “Programmable Quantum Simulators,” that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multidisciplinary collaborations with resources for quantum simulator software, hardware, and education.This document is a summary from a U.S. National Science Foundation supported workshop held on 16–17 September 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum simulators over the next 2–5 years.
    Bibtex

    @Article{altman:quantum_2021, title = {Quantum Simulators: Architectures and Opportunities}, author = {Altman, Ehud and Brown, Kenneth R. and Carleo, Giuseppe and Carr, Lincoln D. and Demler, Eugene and Chin, Cheng and DeMarco, Brian and Economou, Sophia E. and Eriksson, Mark A. and Fu, Kai-Mei C. and Greiner, Markus and Hazzard, Kaden R.A. and Hulet, Randall G. and Koll\'ar, Alicia J. and Lev, Benjamin L. and Lukin, Mikhail D. and Ma, Ruichao and Mi, Xiao and Misra, Shashank and Monroe, Christopher and Murch, Kater and Nazario, Zaira and Ni, Kang-Kuen and Potter, Andrew C. and Roushan, Pedram and Saffman, Mark and Schleier-Smith, Monika and Siddiqi, Irfan and Simmonds, Raymond and Singh, Meenakshi and Spielman, I.B. and Temme, Kristan and Weiss, David S. and Vu\ifmmode \check{c}\else \v{c}\fi{}kovi\ifmmode \acute{c}\else \'{c}\fi{}, Jelena and Vuleti\ifmmode \acute{c}\else \'{c}\fi{}, Vladan and Ye, Jun and Zwierlein, Martin}, journal = {PRX Quantum}, volume = {2}, issue = {1}, pages = {017003}, numpages = {19}, year = {2021}, month = {Feb}, publisher = {American Physical Society}, doi = {10.1103/PRXQuantum.2.017003}, url = {https://link.aps.org/doi/10.1103/PRXQuantum.2.017003} }
64. Thermodynamics and magnetism in the 2D-3D crossover of the Hubbard model
    Eduardo Ibarra-García-Padilla, Rick Mukherjee, Randall G. Hulet, Kaden R. A. Hazzard, Thereza Paiva, and Richard T. Scalettar
    Physical Review A 102, 033340 (2020) (arxiv:2006.02029, pdf)
    
    Summary

    The realization of antiferromagnetic (AF) correlations in ultracold fermionic atoms on an optical lattice is a significant achievement. Experiments have been carried out in one, two, and three dimensions, and have also studied anisotropic configurations with stronger tunneling in some lattice directions. Such anisotropy is relevant to the physics of cuprate superconductors and other strongly correlated materials. Moreover, this anisotropy might be harnessed to enhance AF order. Here we numerically investigate, using the determinant quantum Monte Carlo method, a simple realization of anisotropy in the three-dimensional (3D) Hubbard model in which the tunneling between planes, t⊥, is unequal to the intraplane tunneling t. This model interpolates between the three-dimensional isotropic (t⊥=t) and two-dimensional (2D; t⊥=0) systems. We show that at fixed interaction strength to tunneling ratio (U/t), anisotropy can enhance the magnetic structure factor relative to both 2D and 3D results. However, this enhancement occurs at interaction strengths below those for which the Néel temperature TNˊeel is largest, in such a way that the structure factor cannot be made to exceed its value in isotropic 3D systems at the optimal U/t. We characterize the 2D-3D crossover in terms of the magnetic structure factor, real space spin correlations, number of doubly occupied sites, and thermodynamic observables. An interesting implication of our results stems from the entropy's dependence on anisotropy. As the system evolves from 3D to 2D, the entropy at a fixed temperature increases. Correspondingly, at fixed entropy, the temperature will decrease going from 3D to 2D. This suggests a cooling protocol in which the dimensionality is adiabatically changed from 3D to 2D.
    Bibtex

    @article{ibarra-garcia-padilla:thermodynamics_2020, title = {Thermodynamics and magnetism in the two-dimensional to three-dimensional crossover of the Hubbard model}, author = {Ibarra-Garc\'{\i}a-Padilla, Eduardo and Mukherjee, Rick and Hulet, Randall G. and Hazzard, Kaden R. A. and Paiva, Thereza and Scalettar, Richard T.}, journal = {Phys. Rev. A}, volume = {102}, issue = {3}, pages = {033340}, numpages = {13}, year = {2020}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.102.033340}, url = {https://link.aps.org/doi/10.1103/PhysRevA.102.033340} }
63. Spin-imbalanced ultracold Fermi gases in a two-dimensional array of tubes
    Bhuvanesh Sundar, Jacob A. Fry, Melissa C. Revelle, Randall G. Hulet, and Kaden R. A. Hazzard
    Physical Review A 102, 033311 (2020) (arxiv:2005.01826, pdf)
    
    Summary

    Motivated by a recent experiment Revelle et al., [Phys. Rev. Lett. 117, 235301 (2016)] that characterized the one- to three-dimensional crossover in a spin-imbalanced ultracold gas of 6 Li atoms trapped in a two-dimensional array of tunnel-coupled tubes, we calculate the phase diagram for this system by using Hartree-Fock Bogoliubov-de Gennes mean-field theory and compare the results with experimental data. Mean-field theory predicts fully-spin-polarized normal, partially-spin-polarized normal, spin-polarized superfluid, and spin-balanced superfluid phases in a homogeneous system. We use the local density approximation to obtain density profiles of the gas in a harmonic trap. We compare these calculations with experimental measurements in Revelle et al. as well as previously unpublished data. Our calculations qualitatively agree with experimentally measured densities and coordinates of the phase boundaries in the trap and quantitatively agree with experimental measurements at moderate-to-large polarizations. Our calculations also reproduce the experimentally observed universal scaling of the phase boundaries for different scattering lengths at a fixed value of scaled intertube tunneling. However, our calculations have quantitative differences with experimental measurements at low polarization and fail to capture important features of the one- to three-dimensional crossover observed in experiments. These suggest the important role of physics beyond mean-field theory in the experiments. We expect that our numerical results will aid future experiments in narrowing the search for the Fulde-Ferrell-Larkin-Ovchinnikov phase.
    Bibtex

    @article{sundar:spin-imbalanced_2020, title = {Spin-imbalanced ultracold Fermi gases in a two-dimensional array of tubes}, author = {Sundar, Bhuvanesh and Fry, Jacob A. and Revelle, Melissa C. and Hulet, Randall G. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {102}, issue = {3}, pages = {033311}, numpages = {12}, year = {2020}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.102.033311}, url = {https://link.aps.org/doi/10.1103/PhysRevA.102.033311} }
62. Tightening the Lieb-Robinson bound in locally interacting systems
    Zhiyuan Wang and Kaden R. A. Hazzard
    PRX Quantum 1, 010303 (2020) (arxiv:1908.03997, pdf)
    
    In the News
    "Quantum leap for speed limit bounds", Rice University News
    (also on phys.org, ScienceDaily, EurekAlert, bioengineer.com, ...)
    Summary

    The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective "light cone" decays exponentially with distance from the light-cone front, which expands at finite velocity. Despite being a fundamental result, existing bounds are often extremely loose, limiting their applications when quantitative accuracy is necessary. We derive improved LR bounds in systems with finite-range interactions that qualitatively strengthen previous bounds in two ways: (1) Our bound takes the new form ∥[A^X(t),B^Y(0)]∥≤C(ut/dXY)dXY, much better than the previous exponential form in the large distance dXY→∞ and small time t→0 regions, and is often tight asymptotically. (2) Our method directly leads to both qualitative and quantitative improvements in the LR velocity. Examples of this we demonstrate are that in the Heisenberg XYZ model with spin S, we find v≤const. compared to the previous v∝S which diverges at large S; in Wen's d-dimensional quantum rotor model with large spin S, we find v≤const.d−−√ instead of previous v∝Sd; in multiorbital Hubbard models with N orbitals, we find v∝N−−√ compared to previous v∝N; in the two-dimensional (2D) transverse field Ising model (TFIM) with coupling strength J and transverse field h, we find v≤min{4.27Jh−−−√,15.1J,12.1h} instead of previous v≤43.5J; and for the d-dimensional TFIM our speed scales as v∼d−−√ instead of previous v∼d. These improved LR speeds also allow us to prove a finite upper bound on ground state correlation length in some nontrivial limits where the previous bounds diverge.
    Bibtex

    @article{wang:tightening_2020, title = {Tightening the Lieb-Robinson Bound in Locally Interacting Systems}, author = {Wang, Zhiyuan and Hazzard, Kaden R.A.}, journal = {PRX Quantum}, volume = {1}, issue = {1}, pages = {010303}, numpages = {24}, year = {2020}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PRXQuantum.1.010303}, url = {https://link.aps.org/doi/10.1103/PRXQuantum.1.010303} }
61. Numerical linked cluster expansions for inhomogeneous systems
    Johann Gan and Kaden R. A. Hazzard
    Physical Review A 102, 013318 (2020) (arxiv:2005.03177, pdf)
    
    Summary

    We develop a numerical linked cluster expansion (NLCE) method that can be applied directly to inhomogeneous systems, for example, Hamiltonians with disorder and dynamics initiated from inhomogeneous initial states. We demonstrate the method by calculating dynamics for single-spin expectations and spin correlations in two-dimensional spin models on a square lattice, starting from a checkerboard state. We show that NLCE can give moderate to dramatic improvement over an exact diagonalization of comparable computational cost and that the advantage in computational resources grows exponentially as the size of the clusters included grows. Although the method applies to any type of NLCE, our explicit benchmarks use the rectangle expansion. Besides showing the capability to treat inhomogeneous systems, these benchmarks demonstrate the rectangle expansion's utility out of equilibrium.
    Bibtex

    @Article{gan:numerical_2020, title = {Numerical linked cluster expansions for inhomogeneous systems}, author = {Gan, Johann and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {102}, issue = {1}, pages = {013318}, numpages = {9}, year = {2020}, month = {Jul}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.102.013318}, url = {https://link.aps.org/doi/10.1103/PhysRevA.102.013318} }
60. Collective modes of ultracold fermionic alkaline-earth gases with SU($N$) symmetry
    Sayan Choudhury, Kazi R. Islam, Yanhua Hou, Jim A. Aman, Thomas C. Killian, and Kaden R. A. Hazzard
    Phys. Rev. A 101, 053612 (2020) (arxiv:2001.09503, pdf)
    
    Summary

    We calculate the collective modes of ultracold trapped alkaline-earth-metal fermionic atoms, which possess an SU(N) symmetry of the nuclear spin degree of freedom and a controllable N, with N as large as 10. We calculate the breathing and quadrupole modes of two-dimensional and three-dimensional harmonically trapped gases in the normal phase. We particularly concentrate on two-dimensional gases, where the shift is more accessible experimentally, and the physics has special features. We present results as a function of temperature, interaction strength, density, and N. We include calculations across the collisionless to hydrodynamic crossover. We assume the gas is interacting weakly, such that it can be described by a Boltzmann-Vlasov equation that includes both mean-field terms and the collision integral. We solve this with an approximate scaling ansatz, taking care in two dimensions to preserve the scaling symmetry of the system. We predict the collective-mode frequency shifts and damping, showing that these are measurable in experimentally relevant regimes. We expect these results to furnish powerful tools to characterize interactions and the state of alkaline-earth-metal gases, as well as to lay the foundation for future work, for example, on strongly interacting gases and SU(N) spin modes.
    Bibtex

    @Article{choudhury:collective_2020, title = {Collective modes of ultracold fermionic alkaline-earth-metal gases with SU($N$) symmetry}, author = {Choudhury, Sayan and Islam, Kazi R. and Hou, Yanhua and Aman, Jim A. and Killian, Thomas C. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {101}, issue = {5}, pages = {053612}, numpages = {10}, year = {2020}, month = {May}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.101.053612}, url = {https://link.aps.org/doi/10.1103/PhysRevA.101.053612} }
59. Correlations generated from high-temperature states: Nonequilibrium dynamics in the Fermi-Hubbard model
    Ian G. White, Randall G. Hulet, and Kaden R. A. Hazzard
    Physical Review A 100, 033612 (2019) (arxiv:1612.05671, pdf)
    
    Summary

    We study interaction quenches of the Fermi-Hubbard model initiated from various high-temperature and high-energy states, motivated by cold atom experiments, which currently operate above the ordering temperature(s). We analytically calculate the dynamics for quenches from these initial states, which are often strongly interacting, to the noninteracting limit. Even for high-temperature uncorrelated initial states, transient connected correlations develop. These correlations share many features for all considered initial states. We observe light-cone spreading of intertwined spin and density correlations. The character of these correlations is quite different from their low-temperature equilibrium counterparts: for example, the spin correlations can be ferromagnetic. We also show that an initially localized hole defect affects spin correlations near the hole, suppressing their magnitude and changing their sign.
    Bibtex

    @Article{white:correlations_2016, title = {Correlations generated from high-temperature states: Nonequilibrium dynamics in the Fermi-Hubbard model}, author = {White, Ian G. and Hulet, Randall G. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {100}, issue = {3}, pages = {033612}, numpages = {10}, year = {2019}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.100.033612}, url = {https://link.aps.org/doi/10.1103/PhysRevA.100.033612} } }
58. High-intensity two-frequency photoassociation spectroscopy of a weakly bound molecular state: Theory and experiment
    W. Y. Kon, J. A. Aman, J. C. Hill, T. C. Killian, and Kaden R. A. Hazzard
    Physical Review A 100, 013408 (2019) (arxiv:1812.11682, pdf)
    
    Summary

    We investigate two-frequency photoassociation of a weakly bound molecular state, focusing on a regime where the AC Stark shift is comparable to the halo-state energy. In this “high-intensity” regime, we observe features absent in low-intensity two-frequency photoassociation. We experimentally measure the spectra of Sr86 atoms coupled to the least bound state of the Sr286 ground electronic channel through an intermediate electronically excited molecular state. We compare the spectra to a simple three-level model that includes a two-frequency drive on each leg of the transition. With numerical solution of the time-dependent Schrödinger equation, we show that this model accurately captures (1) the existence of experimentally observed satellite peaks that arise from nonlinear processes, (2) the locations of the two-photon peak in the spectrum, including AC Stark shifts, and (3) in some cases, spectral line shapes. To better understand these numerical results, we develop an approximate treatment of this model, based on Floquet and perturbation theory, that gives simple formulas that accurately capture the halo-state energies. We expect these expressions to be valuable tools to analyze and guide future two-frequency photoassociation experiments.
    Bibtex

    @article{kon:high-intensity_2019, title = {High-intensity two-frequency photoassociation spectroscopy of a weakly bound molecular state: Theory and experiment}, author = {Kon, W. Y. and Aman, J. A. and Hill, J. C. and Killian, T. C. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {100}, issue = {1}, pages = {013408}, numpages = {11}, year = {2019}, month = {Jul}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.100.013408}, url = {https://link.aps.org/doi/10.1103/PhysRevA.100.013408} }
57. Cold atoms in optical lattices
    Kaden R. A. Hazzard and Bhuvanesh Sundar
    Invited review; Chapter in ``2D Quantum Mechanics: Proceedings of the 2018 NIST Workshop" on 2D meta-materials, ed. W. P. Kirk, J. N. Randall, and J. H. G. Owen (2019) (pdf -- our sections only)
    
    Summary

    A introduction to and review of cold atoms in optical lattices, and thoughts on their legacy, limitations, and prospects. Focused on introducing to non-practitioners, in the context of a 2D quantum meta-materials workshop discussing comparative capabilities with other quantum simulation platforms, especially atomically precise Si:P materials.
    Bibtex

    @INBOOK{hazzard:cold_2019, chapter = {Cold Atoms in Optical Lattices}, title = {2D Quantum Mechanics: Proceedings of the 2018 NIST Workshop}, publisher = {World Scientific}, year = {2019}, editor = {Wiley P. Kirk and John N. Randall and James H. G. Owen }, author = {Kaden R. A. Hazzard and Bhuvanesh Sundar} }
56. Analysis of continuous and discrete Wigner approximations for spin dynamics
    Bhuvanesh Sundar, Kenneth C. Wang, and Kaden R. A. Hazzard
    Physical Review A 99, 043627 (2019) (arxiv:1807.02171, pdf)
    
    Summary

    We compare the continuous and discrete truncated Wigner approximations of various spin models' dynamics to exact analytical and numerical solutions. We account for all components of spin-spin correlations on equal footing, facilitated by a recently introduced geometric correlation matrix visualization technique [Mukherjee et al., Phys. Rev. A 97, 043606 (2018)]. We find that at modestly short times, the dominant error in both approximations is to substantially suppress spin correlations along one direction.
    Bibtex

    @Article{sundar:analysis_2019, title = {Analysis of continuous and discrete Wigner approximations for spin dynamics}, author = {Sundar, Bhuvanesh and Wang, Kenneth C. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {99}, issue = {4}, pages = {043627}, numpages = {17}, year = {2019}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.99.043627}, url = {https://link.aps.org/doi/10.1103/PhysRevA.99.043627} }
55. A traffic jam of light
    Kaden R. A. Hazzard
    Nature 566, 45 (2019) (pdf)
    invited News & Views article
    
    Summary

    A technique that harnesses energy loss has been used to produce a phase of matter in which particles of light are locked in place. This opens a path to realizing previously unseen exotic phases of matter.
    Bibtex

    @article{hazzard:traffic_2019, title = {A traffic jam of light}, author = {Hazzard, Kaden R. A.}, journal = {Nature}, volume = {566}, pages = {45}, year = {2019} }
54. Strings of ultracold molecules in a synthetic dimension
    B. Sundar, M. Thibodeau, Z. Wang, B. Gadway, and K. R. A. Hazzard
    Physical Review A 99, 013624 (2019) (arxiv:1812.02229, pdf)
    
    Summary

    We consider ultracold polar molecules trapped in a unit-filled one-dimensional chain in real space created with an optical lattice or a tweezer array and illuminated by microwaves that resonantly drive transitions within a chain of rotational states. We describe the system by a two-dimensional lattice model, with the first dimension being a lattice in real space and the second dimension being a lattice in a synthetic direction composed of rotational states. We calculate this system’s ground-state phase diagram. We show that as the dipole interaction strength is increased, the molecules undergo a phase transition from a two-dimensional gas to a phase in which the molecules bind together and form a string that resembles a one-dimensional object living in the two-dimensional (i.e., one real and one synthetic dimensional) space. We demonstrate this with two complementary techniques: numerical calculations using matrix product state techniques and an analytic solution in the limit of infinitely strong dipole interaction. Our calculations reveal that the string phase at infinite interaction is effectively described by emergent particles living on the string and that this leads to a rich spectrum with excitations missed in earlier mean-field treatments.
    Bibtex

    @article{sundar:strings_2019, title = {Strings of ultracold molecules in a synthetic dimension}, author = {Sundar, Bhuvanesh and Thibodeau, Matthew and Wang, Zhiyuan and Gadway, Bryce and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {99}, issue = {1}, pages = {013624}, numpages = {11}, year = {2019}, month = {Jan}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.99.013624}, url = {https://link.aps.org/doi/10.1103/PhysRevA.99.013624} }
53. A Model for Scattering with Proliferating Resonances: Many Coupled Square Wells
    Nirav P. Mehta, Kaden R. A. Hazzard, and Christopher Ticknor
    Phys. Rev. A 98, 062703 (2018) (arxiv:1809.06900, pdf)
    
    Summary

    We present a multichannel model for elastic interactions, composed of an arbitrary number of coupled finite square-well potentials, and derive semianalytic solutions for its scattering behavior. Despite the model's simplicity, it is flexible enough to include many coupled short-ranged resonances in the vicinity of the collision threshold, as is necessary to describe ongoing experiments in ultracold molecules and lanthanide atoms. We also introduce a simple but physically realistic statistical ensemble for parameters in this model. We compute the resulting probability distributions of nearest-neighbor resonance spacings and analyze them by fitting to the Brody distribution. We quantify the ability of alternative distribution functions, for resonance spacing and resonance number variance, to describe the crossover regime. The analysis demonstrates that the multichannel square-well model with the chosen ensemble of parameters naturally captures the crossover from integrable to chaotic scattering as a function of closed-channel coupling strength.
    Bibtex

    @article{mehta:model_2018, title = {Model for scattering with proliferating resonances: Many coupled square wells}, author = {Mehta, Nirav P. and Hazzard, Kaden R. A. and Ticknor, Christopher}, journal = {Phys. Rev. A}, volume = {98}, issue = {6}, pages = {062703}, numpages = {15}, year = {2018}, month = {Dec}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.98.062703}, url = {https://link.aps.org/doi/10.1103/PhysRevA.98.062703} }
52. 

    Photoassociative Spectroscopy of a Halo Molecule in 86Sr
    J. A. Aman, J. C. Hill, R. Ding, K. R. A. Hazzard, T. C. Killian, and W. Y. Kon,
    Phys. Rev. A 98, 053441 (2018) ["Editor's Suggestion"]
    (arxiv:1809.09267, pdf)
    

    Summary

    We present two-photon photoassociation to the least-bound vibrational level of the X1Σ+g electronic ground state of the 86Sr2 dimer and measure a binding energy of Eb=−83.00(7)(20)\,kHz. Because of the very small binding energy, this is a halo state corresponding to the scattering resonance for two 86Sr atoms at low temperature. The measured binding energy, combined with universal theory for a very weakly bound state on a potential that asymptotes to a van der Waals form, is used to determine an s-wave scattering length a=810.6(12)\,a0, which is consistent with, but substantially more accurate than the previously determined a=798(12)a0 found from mass-scaling and precision spectroscopy of other Sr isotopes. For the intermediate state, we use a bound level on the metastable 1S0−3P1 potential. Large sensitivity of the dimer binding energy to light near-resonant with the bound-bound transition to the intermediate state suggests that 86Sr has great promise for manipulating atom interactions optically and probing naturally occurring Efimov states.

    Bibtex

    @article{aman:photoassociative_2018, title = {Photoassociative spectroscopy of a halo molecule in $^{86}\mathrm{Sr}$}, author = {Aman, J. A. and Hill, J. C. and Ding, R. and Hazzard, Kaden R. A. and Killian, T. C. and Kon, W. Y.}, journal = {Phys. Rev. A}, volume = {98}, issue = {5}, pages = {053441}, numpages = {9}, year = {2018}, month = {Nov}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.98.053441}, url = {https://link.aps.org/doi/10.1103/PhysRevA.98.053441} }
51. Cooling fermions in an optical lattice by adiabatic demagnetization
    Anthony E. Mirasola, Michael L. Wall, and Kaden R. A. Hazzard
    Phys. Rev. A 98, 033607 (2018) (arxiv:1806.02948, pdf)
    
    Summary

    The Fermi-Hubbard model describes ultracold fermions in an optical lattice and exhibits antiferromagnetic long-ranged order below the Néel temperature. However, reaching this temperature in the laboratory has remained an elusive goal. In other atomic systems, such as trapped ions, low temperatures have been successfully obtained by adiabatic demagnetization, in which a strong effective magnetic field is applied to a spin-polarized system and the magnetic field is adiabatically reduced to zero. Unfortunately, applying this approach to the Fermi-Hubbard model encounters a fundamental obstacle: the SU(2) symmetry introduces many level crossings that prevent the system from reaching the ground state, even in principle. However, by breaking the SU(2) symmetry with a spin-dependent tunneling, we show that adiabatic demagnetization can achieve low-temperature states. Using density matrix renormalization group (DMRG) calculations in one dimension, we numerically find that demagnetization protocols successfully reach low-temperature states of a spin-anisotropic Hubbard model, and we discuss how to optimize this protocol for experimental viability. By subsequently ramping spin-dependent tunnelings to spin-independent tunnelings, we expect that our protocol can be employed to produce low-temperature states of the Fermi-Hubbard model.
    Bibtex

    @article{mirasola:cooling_2018, title = {Cooling fermions in an optical lattice by adiabatic demagnetization}, author = {Mirasola, Anthony E. and Wall, Michael L. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {98}, issue = {3}, pages = {033607}, numpages = {8}, year = {2018}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.98.033607}, url = {https://link.aps.org/doi/10.1103/PhysRevA.98.033607} }
50. Bosonic molecules in a lattice: Unusual fluid phase from multichannel interactions
    Kevin D. Ewart, Michael L. Wall, and Kaden R. A. Hazzard
    Phys. Rev. A 98, 013611 (2018) (arxiv:1706.00539, pdf)
    
    Summary

    We show that multichannel interactions significantly alter the phase diagram of ultracold bosonic molecules in an optical lattice. Most prominently, an unusual fluid region intervenes between the conventional superfluid and the Mott insulator. In it, number fluctuations remain but phase coherence is suppressed by a significant factor. This factor can be made arbitrarily large, at least in a two-site configuration. We calculate the phase diagram using complementary methods, including Gutzwiller mean-field and density-matrix renormalization group calculations. Although we focus on bosonic molecules without dipolar interactions, we expect multichannel interactions to remain important for dipolar interacting and fermionic molecules.
    Bibtex

    @article{PhysRevA.98.013611, title = {Bosonic molecules in a lattice: Unusual fluid phase from multichannel interactions}, author = {Ewart, Kevin D. and Wall, Michael L. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {98}, issue = {1}, pages = {013611}, numpages = {6}, year = {2018}, month = {Jul}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.98.013611}, url = {https://link.aps.org/doi/10.1103/PhysRevA.98.013611} } }
49. Viewpoint: Watching a quantum magnet grow in ultracold atoms
    Kaden R. A. Hazzard
    Physics 11, 63 (2018) (pdf)
    
    Summary

    Two experiments watch an antiferromagnetic phase of matter emerge in ultracold Rydberg atoms, opening up a new platform for quantum simulation.
    Bibtex

    @article{viewpoint-watching:hazzard_2018, title = {Viewpoint: Watching a quantum magnet grow in ultracold atoms}, author = {Hazzard, Kaden R. A.}, journal = {Physics}, volume = {1}, pages = {63}, year = {2018}, month = {June}, publisher = {American Physical Society} }
48. Complex-network description of thermal quantum states in the Ising spin chain
    Bhuvanesh Sundar, Marc Andrew Valdez, Lincoln D. Carr, and Kaden R. A. Hazzard
    Phys. Rev. A 97, 052320 (2018) (arXiv:1803.00994, pdf)
    
    Summary

    We use network analysis to describe and characterize an archetypal quantum system—an Ising spin chain in a transverse magnetic field. We analyze weighted networks for this quantum system, with link weights given by various measures of spin-spin correlations such as the von Neumann and Rényi mutual information, concurrence, and negativity. We analytically calculate the spin-spin correlations in the system at an arbitrary temperature by mapping the Ising spin chain to fermions, as well as numerically calculate the correlations in the ground state using matrix product state methods, and then analyze the resulting networks using a variety of network measures. We demonstrate that the network measures show some traits of complex networks already in this spin chain, arguably the simplest quantum many-body system. The network measures give insight into the phase diagram not easily captured by more typical quantities, such as the order parameter or correlation length. For example, the network structure varies with transverse field and temperature, and the structure in the quantum critical fan is different from the ordered and disordered phases.
    Bibtex

    @article{PhysRevA.97.052320, title = {Complex-network description of thermal quantum states in the Ising spin chain}, author = {Sundar, Bhuvanesh and Valdez, Marc Andrew and Carr, Lincoln D. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {97}, issue = {5}, pages = {052320}, numpages = {10}, year = {2018}, month = {May}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.97.052320}, url = {https://link.aps.org/doi/10.1103/PhysRevA.97.052320} }
47. Geometric representation of spin correlations and applications to ultracold systems
    Rick Mukherjee, Anthony E. Mirasola, Jacob Hollingsworth, Ian G. White, and Kaden R. A. Hazzard
    Phys. Rev. A 97, 043606 (2018) (arxiv:1612.06459, pdf, supplemental movies)
    
    Summary

    We provide a one-to-one map between the spin correlations and certain three-dimensional shapes, analogous to the map between single spins and Bloch vectors, and demonstrate its utility. Much as one can reason geometrically about dynamics using a Bloch vector -- e.g., a magnetic field causes it to precess and dissipation causes it to shrink -- one can reason similarly about the shapes we use to visualize correlations. This visualization demonstrates its usefulness by unveiling the hidden structure in the correlations. For example, seemingly complex correlation dynamics can be described as simple motions of the shapes. We demonstrate the simplicity of the dynamics, which is obscured in conventional analyses, by analyzing several physical systems of relevance to cold atoms.
    Bibtex

    @article{mukherjee:geometric_2018, title = {Geometric representation of spin correlations and applications to ultracold systems}, author = {Mukherjee, Rick and Mirasola, Anthony E. and Hollingsworth, Jacob and White, Ian G. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {97}, issue = {4}, pages = {043606}, numpages = {13}, year = {2018}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.97.043606}, url = {https://link.aps.org/doi/10.1103/PhysRevA.97.043606} }
46. Analytic ground state wave functions of mean-field p_x + i p_y superconductors with vortices and boundaries
    Zhiyuan Wang and Kaden R. A. Hazzard
    Phys. Rev. B 97, 104501 (2018) (arxiv:1712.09904, pdf)
    
    Summary

    We study Read and Green's mean-field model of the spinless px+ipy superconductor [N. Read and D. Green, Phys. Rev. B 61, 10267 (2000)] at a special set of parameters where we find the analytic expressions for the topologically degenerate ground states and the Majorana modes, including in finite systems with edges and in the presence of an arbitrary number of vortices. The wave functions of these ground states are similar (but not always identical) to the Moore-Read Pfaffian states proposed for the ν=52 fractional quantum Hall system, which are interpreted as the p-wave superconducting states of composite fermions. The similarity in the long-wavelength universal properties is expected from previous work, but at the special point studied herein the wave functions are exact even for short-range, nonuniversal properties. As an application of these results, we show how to obtain the non-Abelian statistics of the vortex Majorana modes by explicitly calculating the analytic continuation of the ground state wave functions when vortices are adiabatically exchanged, an approach different from the previous one based on universal arguments. Our results are also useful for constructing particle-number-conserving (and interacting) Hamiltonians with exact projected mean-field states.
    Bibtex

    @article{PhysRevB.97.104501, title = {Analytic ground state wave functions of mean-field ${p}_{x}+i{p}_{y}$ superconductors with vortices and boundaries}, author = {Wang, Zhiyuan and Hazzard, Kaden R. A.}, journal = {Phys. Rev. B}, volume = {97}, issue = {10}, pages = {104501}, numpages = {15}, year = {2018}, month = {Mar}, publisher = {American Physical Society}, doi = {10.1103/PhysRevB.97.104501}, url = {https://link.aps.org/doi/10.1103/PhysRevB.97.104501} }
45. Synthetic dimensions in ultracold polar molecules
    Bhuvanesh Sundar, Bryce Gadway, and Kaden R. A. Hazzard
    Scientific Reports 8, 3422 (2018) (arxiv:1708.02112, pdf)
    
    Summary

    Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic dimensions have been engineered in ongoing experiments with ultracold matter. We show that rotational states of ultracold molecules can be used as synthetic dimensions extending to many – potentially hundreds of – synthetic lattice sites. Microwaves coupling rotational states drive fully controllable synthetic inter-site tunnelings, enabling, for example, topological band structures. Interactions leads to even richer behavior: when molecules are frozen in a real space lattice with uniform synthetic tunnelings, dipole interactions cause the molecules to aggregate to a narrow strip in the synthetic direction beyond a critical interaction strength, resulting in a quantum string or a membrane, with an emergent condensate that lives on this string or membrane. All these phases can be detected using local measurements of rotational state populations.
    Bibtex

    @Article{sundar:synthetic_2018, author = {Bhuvanesh Sundar and Bryce Gadway and Kaden R. A. Hazzard}, title = {Synthetic dimensions in ultracold polar molecules}, journal = {Scientific Reports}, volume = {8}, pages = {3422}, year = {2018} }
44. Correlations and enlarged superconducting phase of t-J_⊥ chains of ultracold molecules on optical lattices
    Salvatore R. Manmana, Marcel Möller, Riccardo Gezzi, and Kaden R. A. Hazzard
    Phys. Rev. A 96, 043618 (2017) (arxiv:1707.00343, pdf)
    
    Summary

    We compute physical properties across the phase diagram of the t−J⊥ chain with long-range dipolar interactions, which describe ultracold polar molecules on optical lattices. Our results obtained by the density-matrix renormalization group indicate that superconductivity is enhanced when the Ising component $J_z$ of the spin-spin interaction and the charge component V are tuned to zero and even further by the long-range dipolar interactions. At low densities, a substantially larger spin gap is obtained. We provide evidence that long-range interactions lead to algebraically decaying correlation functions despite the presence of a gap. Although this has recently been observed in other long-range interacting spin and fermion models, the correlations in our case have the peculiar property of having a small and continuously varying exponent. We construct simple analytic models and arguments to understand the most salient features.
    Bibtex

    @article{PhysRevA.96.043618, title = {Correlations and enlarged superconducting phase of $t\ensuremath{-}{J}_{\ensuremath{\perp}}$ chains of ultracold molecules on optical lattices}, author = {Manmana, Salvatore R. and M\"oller, Marcel and Gezzi, Riccardo and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {96}, issue = {4}, pages = {043618}, numpages = {14}, year = {2017}, month = {Oct}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.96.043618}, url = {https://link.aps.org/doi/10.1103/PhysRevA.96.043618} }
43. Number-conserving interacting fermion models with exact topological superconducting ground states
    Zhiyuan Wang, Youjiang Xu, Han Pu, and Kaden R. A. Hazzard
    Phys. Rev. B 96, 115110 (2017) (arxiv:1703.01249, pdf)
    
    Summary

    We present a method to construct number-conserving Hamiltonians whose ground states exactly reproduce an arbitrarily chosen BCS-type mean-field state. Such parent Hamiltonians can be constructed not only for the usual s-wave BCS state, but also for more exotic states of this form, including the ground states of Kitaev wires and two-dimensional topological superconductors. This method leads to infinite families of locally interacting fermion models with exact topological superconducting ground states. After explaining the general technique, we apply this method to construct two specific classes of models. The first one is a one-dimensional double wire lattice model with Majorana-like degenerate ground states. The second one is a two-dimensional px+ipy superconducting model, where we also obtain analytic expressions for topologically degenerate ground states in the presence of vortices. Our models may provide a deeper conceptual understanding of how Majorana zero modes could emerge in condensed matter systems, as well as inspire novel routes to realize them in experiment.
    Bibtex

    @Article{wang:number-conserving_2017, title = {Number-conserving interacting fermion models with exact topological superconducting ground states}, author = {Wang, Zhiyuan and Xu, Youjiang and Pu, Han and Hazzard, Kaden R. A.}, journal = {Phys. Rev. B}, volume = {96}, issue = {11}, pages = {115110}, numpages = {9}, year = {2017}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevB.96.115110}, url = {https://link.aps.org/doi/10.1103/PhysRevB.96.115110} }
42. Lattice-model parameters for ultracold nonreactive molecules: Chaotic scattering and its limitations
    Michael L. Wall, Rick Mukherjee, Shah Saad Alam, Nirav P. Mehta, and Kaden R. A. Hazzard
    Phys. Rev. A 95, 043636 (2017) (arxiv:1612.06943, pdf)
    
    Summary

    We calculate the parameters of the recently derived many-channel Hubbard model that is predicted to describe ultracold nonreactive molecules in an optical lattice, going beyond the approximations used by Doçaj et al. [A. Doçaj et al., Phys. Rev. Lett. 116, 135301 (2016)]. Although those approximations are expected to capture the qualitative structure of the model parameters, finer details and quantitative values are less certain. To set expectations for experiments, whose results depend on the model parameters, we describe the approximations' regime of validity and the likelihood that experiments will be in this regime, discuss the impact that the failure of these approximations would have on the predicted model, and develop theories going beyond these approximations. Not only is it necessary to know the model parameters in order to describe experiments, but the connection that we elucidate between these parameters and the underlying assumptions that are used to derive them will allow molecule experiments to probe new physics. For example, transition state theory, which is used across chemistry and chemical physics, plays a key role in our determination of lattice parameters, thus connecting its physical assumptions to highly accurate experimental investigation.
    Bibtex

    @article{wall:lattice-model_2017, title = {Lattice-model parameters for ultracold nonreactive molecules: Chaotic scattering and its limitations}, author = {Wall, Michael L. and Mukherjee, Rick and Alam, Shah Saad and Mehta, Nirav P. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {95}, issue = {4}, pages = {043636}, numpages = {20}, year = {2017}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.95.043636}, url = {https://link.aps.org/doi/10.1103/PhysRevA.95.043636} }
41. Microscopic derivation of multichannel Hubbard models for ultracold nonreactive molecules in an optical lattice
    Michael L. Wall, Nirav P. Mehta, Rick Mukherjee, Shah Saad Alam, and Kaden R. A. Hazzard
    Phys. Rev. A 95, 043635 (2017) (arxiv:1612.06942, pdf)
    
    Summary

    Recent experimental advances in the cooling and manipulation of bialkali-metal dimer molecules have enabled the production of gases of ultracold molecules that are not chemically reactive. It has been presumed in the literature that in the absence of an electric field the low-energy scattering of such nonreactive molecules (NRMs) will be similar to atoms, in which a single s-wave scattering length governs the collisional physics. However, Doçaj et al. [Phys.Rev.Lett. 116, 135301 (2016)] argued that the short-range collisional physics of NRMs is much more complex than for atoms and that this leads to a many-body description in terms of a multichannel Hubbard model. In this work we show that this multichannel Hubbard model description of NRMs in an optical lattice is robust against the approximations employed by Doçaj et al. to estimate its parameters. We do so via an exact, albeit formal, derivation of a multichannel resonance model for two NRMs from an ab initio description of the molecules in terms of their constituent atoms. We discuss the regularization of this two-body multichannel resonance model in the presence of a harmonic trap and how its solutions form the basis for the many-body model of Doçaj et al.. We also generalize the derivation of the effective lattice model to include multiple internal states (e.g., rotational or hyperfine). We end with an outlook to future research.
    Bibtex

    @article{wall:microscopic_2017, title = {Microscopic derivation of multichannel Hubbard models for ultracold nonreactive molecules in an optical lattice}, author = {Wall, Michael L. and Mehta, Nirav P. and Mukherjee, Rick and Alam, Shah Saad and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {95}, issue = {4}, pages = {043635}, numpages = {16}, year = {2017}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.95.043635}, url = {https://link.aps.org/doi/10.1103/PhysRevA.95.043635} } }
40. A solid more fluid than a fluid
    Kaden R. A. Hazzard
    Nature 543, 47 (2017) (pdf)
    invited News & Views article
    
    Summary

    A supersolid is a paradoxical and elusive state of matter that has been sought for more than 60 years. Two experiments have now observed its characteristic signatures in ultracold quantum matter.
    Bibtex

    @article{hazzard:solid_2017, title = {A solid more fluid than a fluid}, author = {Hazzard, Kaden R. A.}, journal = {Nature}, volume = {543}, pages = {47}, year = {2017} }
39. Accessing Rydberg-dressed interactions using many-body Ramsey dynamics
    Rick Mukherjee, Thomas C. Killian, and Kaden R. A. Hazzard
    Phys. Rev. A 94, 053422 (2016) (arXiv:1511.08856, pdf)
    
    Summary

    We demonstrate that Ramsey spectroscopy can be used to observe Rydberg-dressed interactions in a many-body system well within experimentally measured lifetimes, in contrast to previous research, which either focused on interactions near Förster resonances or on few-atom systems. We build a spin-1/2 from one level that is Rydberg-dressed and another that is not. These levels may be hyperfine or long-lived electronic states. An Ising spin model governs the Ramsey dynamics, which we demonstrate can be used to characterize the Rydberg-dressed interactions. Furthermore, the dynamics can differ significantly from that observed in other spin systems. As one example, spin echo can increase the rate at which coherence decays. The results also apply to bare (undressed) Rydberg states as a special case, for which we quantitatively reproduce recent ultrafast experiments without fitting.
    Bibtex

    @article{mukherjee:accessing_2016, title = {Accessing Rydberg-dressed interactions using many-body Ramsey dynamics}, author = {Mukherjee, Rick and Killian, Thomas C. and Hazzard, Kaden R. A.}, journal = {Phys. Rev. A}, volume = {94}, issue = {5}, pages = {053422}, numpages = {8}, year = {2016}, month = {Nov}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.94.053422}, url = {http://link.aps.org/doi/10.1103/PhysRevA.94.053422} }
38. Synthetic-gauge-field stabilization of the chiral-spin-liquid phase
    Gang Chen, Kaden R. A. Hazzard, Ana Maria Rey, and Michael Hermele
    Physical Review A 93, 061601(R) (2016) (arXiv:1501.04086, pdf)
    
    Summary

    We explore the phase diagram of the SU(N) Hubbard models describing fermionic alkaline-earth-metal atoms in a square optical lattice with, on average, one atom per site, using a slave rotor mean-field approach. We find that the chiral spin liquid (CSL) predicted for N≥5 and large interactions passes through a fractionalized state with a spinon Fermi surface as interactions are decreased before transitioning to a weakly interacting metal. We show that by adding a uniform artificial gauge field with $2\pi/N$ flux per plaquette, the CSL becomes the ground state for all N≥3 at intermediate interactions, persists to weaker interactions, and exhibits a larger spin gap. For N≥5 we find the CSL is the ground state everywhere the system is a Mott insulator. The gauge field stabilization of the CSL at lower interactions, and thus at weaker lattice depths, together with the increased spin gap, can relax the temperature constraints required for its experimental realization in ultracold atom systems.
    Bibtex

    @article{chen:synthetic_2016, title = {Synthetic-gauge-field stabilization of the chiral-spin-liquid phase}, author = {Chen, Gang and Hazzard, Kaden R. A. and Rey, Ana Maria and Hermele, Michael}, journal = {Phys. Rev. A}, volume = {93}, issue = {6}, pages = {061601}, numpages = {6}, year = {2016}, month = {Jun}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.93.061601}, url = {http://link.aps.org/doi/10.1103/PhysRevA.93.061601} }
37. Ultracold nonreactive molecules in an optical lattice: connecting chemistry to many-body physics
    Andris Doçaj, Michael L. Wall, Rick Mukherjee, and Kaden R. A. Hazzard
    Physical Review Letters 116, 135301 (2016) (arXiv:1512.06177, pdf)
    
    Summary

    We derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model, which is commonly assumed to accurately describe NRMs, we find that the single on-site interaction parameter U is replaced by a multichannel interaction, whose properties we elucidate. Because this arises from complex short-range collisional physics, it requires no dipolar interactions and thus occurs even in the absence of an electric field or for homonuclear molecules. We find a crossover between coherent few-channel models and fully incoherent single-channel models as the lattice depth is increased. We show that the effective model parameters can be determined in lattice modulation experiments, which, consequently, measure molecular collision dynamics with a vastly sharper energy resolution than experiments in a free-space ultracold gas.
    Bibtex

    @article{docaj:ultracold_2016, title = {Ultracold Nonreactive Molecules in an Optical Lattice: Connecting Chemistry to Many-Body Physics}, author = {Do\ifmmode \mbox{\c{c}}\else \c{c}\fi{}aj, Andris and Wall, Michael L. and Mukherjee, Rick and Hazzard, Kaden R. A.}, journal = {Phys. Rev. Lett.}, volume = {116}, issue = {13}, pages = {135301}, numpages = {7}, year = {2016}, month = {Mar}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.116.135301}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.116.135301} }
36. Rydberg-blockade effects in Autler-Townes spectra of ultracold strontium
    B. J. DeSalvo, J. A. Aman, C. Gaul, T. Pohl, S. Yoshida, J. Burgdörfer, K. R. A. Hazzard, F. B. Dunning, and T. C. Killian
    Physical Review A 93, 022709 (2016) (arXiv:1510.08032, pdf)
    
    Summary

    We present a combined experimental and theoretical study of the effects of Rydberg interactions on Autler-Townes spectra of ultracold gases of atomic strontium. Realizing two-photon Rydberg excitation via a long-lived triplet state allows us to probe the regime where Rydberg state decay presents the dominant decoherence mechanism. The effects of Rydberg interactions are observed in shifts, asymmetries, and broadening of the measured atom-loss spectra. The experiment is analyzed within a one-body density-matrix approach, accounting for interaction-induced level shifts and dephasing through nonlinear terms that approximately incorporate correlations due to the Rydberg blockade. This description yields good agreement with our experimental observations for short excitation times. For longer excitation times, the loss spectrum is altered qualitatively, suggesting additional dephasing mechanisms beyond the standard blockade mechanism based on pure van der Waals interactions.
    Bibtex

    @Article{desalvo:Rydberg_2015, title = {Rydberg-blockade effects in Autler-Townes spectra of ultracold strontium}, author = {DeSalvo, B. J. and Aman, J. A. and Gaul, C. and Pohl, T. and Yoshida, S. and Burgd\"orfer, J. and Hazzard, K. R. A. and Dunning, F. B. and Killian, T. C.}, journal = {Phys. Rev. A}, volume = {93}, issue = {2}, pages = {022709}, numpages = {10}, year = {2016}, month = {Feb}, doi = {10.1103/PhysRevA.93.022709}, url = {http://link.aps.org/doi/10.1103/PhysRevA.93.022709} }
35. 

    Effective many-body parameters for atoms in nonseparable Gaussian optical potentials
    Michael L. Wall, Kaden R. A. Hazzard, and Ana Maria Rey
    Physical Review A 92, 013610 (2015) ["Editor's Suggestion"]
    (arXiv:1505.03753, pdf)
    

    Summary

    We analyze the properties of particles trapped in three-dimensional potentials formed from superimposed Gaussian beams, fully taking into account effects of potential anharmonicity and nonseparability. Although these effects are negligible in more conventional optical lattice experiments, they are essential for emerging ultracold-atom developments. We focus in particular on two potentials utilized in current ultracold-atom experiments: arrays of tightly focused optical tweezers and a one-dimensional optical lattice with transverse Gaussian confinement and highly excited transverse modes. Our main numerical tools are discrete variable representations (DVRs), which combine many favorable features of spectral and grid-based methods, such as the computational advantage of exponential convergence and the convenience of an analytical representation of Hamiltonian matrix elements. Optimizations, such as symmetry adaptations and variational methods built on top of DVR methods, are presented and their convergence properties discussed. We also present a quantitative analysis of the degree of nonseparability of eigenstates, borrowing ideas from the theory of matrix product states, leading to both conceptual and computational gains. Beyond developing numerical methodologies, we present results for construction of optimally localized Wannier functions and tunneling and interaction matrix elements in optical lattices and tweezers relevant for constructing effective models for many-body physics.

    Bibtex

    @article{PhysRevA.92.013610, title = {Effective many-body parameters for atoms in nonseparable Gaussian optical potentials}, author = {Wall, Michael L. and Hazzard, Kaden R. A. and Rey, Ana Maria}, journal = {Phys. Rev. A}, volume = {92}, issue = {1}, pages = {013610}, numpages = {18}, year = {2015}, month = {Jul}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.92.013610}, url = {http://link.aps.org/doi/10.1103/PhysRevA.92.013610} }
34. Quantum magnetism with ultracold molecules
    Michael L. Wall, Kaden R. A. Hazzard, and Ana Maria Rey
    Chapter in "From atomic to mesoscale: The Role of Quantum Coherence in Systems of Various Complexities" ed. S. Malinovskaya and I. Novikova World Scientific (2015) [Review article] (arXiv:1406.4758, pdf)
    
    Summary

    This article gives an introduction to the realization of effective quantum magnetism with ultracold molecules in an optical lattice, reviews experimental and theoretical progress, and highlights future opportunities opened up by ongoing experiments. Ultracold molecules offer capabilities that are otherwise difficult or impossible to achieve in other effective spin systems, such as long-ranged spin-spin interactions with controllable degrees of spatial and spin anisotropy and favorable energy scales. Realizing quantum magnetism with ultracold molecules provides access to rich many-body behaviors, including many exotic phases of matter and interesting excitations and dynamics. Far-from-equilibrium dynamics plays a key role in our exposition, just as it did in recent ultracold molecule experiments realizing effective quantum magnetism. In particular, we show that dynamical probes allow the observation of correlated many-body spin physics, even in polar molecule gases that are not quantum degenerate. After describing how quantum magnetism arises in ultracold molecules and discussing recent observations of quantum magnetism with polar molecules, we survey prospects for the future, ranging from immediate goals to long-term visions.
    Bibtex

    @INBOOK{wall:quantum_2015, chapter = {Quantum magnetism with ultracold molecules}, title = {From atomic to mesoscale: The Role of Quantum Coherence in Systems of Various Complexities}, publisher = {World Scientific}, year = {2015}, editor = {S. Malinovskaya and I. Novikova}, author = {Michael L. Wall and Kaden R. A. Hazzard and Ana Maria Rey
    } }
33. Quantum correlations and entanglement in far-from-equilibrium spin systems
    Kaden R. A. Hazzard, Mauritz van den Worm, Michael Foss-Feig, Salvatore R. Manmana, Emanuele G. Dalla Torre, Tilman Pfau, Michael Kastner, and Ana Maria Rey
    Physical Review A 90, 063622 (2014) (arXiv:1406.0937, pdf)
    
    Summary

    By applying complementary analytic and numerical methods, we investigate the dynamics of spin-$1/2$ XXZ models with variable-range interactions in arbitrary dimensions. The dynamics we consider is initiated from uncorrelated states that are easily prepared in experiments; it can be equivalently viewed as either Ramsey spectroscopy or a quantum quench. Our primary focus is the dynamical emergence of correlations and entanglement in these far-from-equilibrium interacting quantum systems: We characterize these correlations by the entanglement entropy, concurrence, and squeezing, which are inequivalent measures of entanglement corresponding to different quantum resources. In one spatial dimension, we show that the time evolution of correlation functions manifests a nonperturbative dynamic singularity. This singularity is characterized by a universal power-law exponent that is insensitive to small perturbations. Explicit realizations of these models in current experiments using polar molecules, trapped ions, Rydberg atoms, magnetic atoms, and alkaline-earth and alkali-metal atoms in optical lattices, along with the relative merits and limitations of these different systems, are discussed.
    Bibtex

    @article{hazzard:quantum_2014, title = {Quantum correlations and entanglement in far-from-equilibrium spin systems}, author = {Hazzard, Kaden R. A. and van den Worm, Mauritz and Foss-Feig, Michael and Manmana, Salvatore R. and Dalla Torre, Emanuele G. and Pfau, Tilman and Kastner, Michael and Rey, Ana Maria}, journal = {Phys. Rev. A}, volume = {90}, issue = {6}, pages = {063622}, numpages = {21}, year = {2014}, month = {Dec}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.90.063622}, url = {http://link.aps.org/doi/10.1103/PhysRevA.90.063622} }
32. Many-body dynamics of dipolar molecules in an optical lattice
    Kaden R. A. Hazzard, Bryce Gadway, Michael Foss-Feig, Bo Yan, Steven A. Moses, Jacob P. Covey, Norman Y. Yao, Mikhail D. Lukin, Jun Ye, Deborah S. Jin, and Ana Maria Rey
    Physical Review Letters 113, 195302 (2014) (arXiv:1402.2354, pdf)
    
    Summary

    We use Ramsey spectroscopy to experimentally probe the quantum dynamics of disordered dipolar-interacting ultracold molecules in a partially filled optical lattice, and we compare the results to theory. We report the capability to control the dipolar interaction strength. We find excellent agreement between our measurements of the spin dynamics and theoretical calculations with no fitting parameters, including the dynamics’ dependence on molecule number and on the dipolar interaction strength. This agreement verifies the microscopic model expected to govern the dynamics of dipolar molecules, even in this strongly correlated beyond-mean-field regime, and represents the first step towards using this system to explore many-body dynamics in regimes that are inaccessible to current theoretical techniques.
    Bibtex

    @article{hazzard:many-body_2014, title = {Many-Body Dynamics of Dipolar Molecules in an Optical Lattice}, author = {Hazzard, Kaden R. A. and Gadway, Bryce and Foss-Feig, Michael and Yan, Bo and Moses, Steven A. and Covey, Jacob P. and Yao, Norman Y. and Lukin, Mikhail D. and Ye, Jun and Jin, Deborah S. and Rey, Ana Maria}, journal = {Phys. Rev. Lett.}, volume = {113}, issue = {19}, pages = {195302}, numpages = {5}, year = {2014}, month = {Nov}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.113.195302}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.113.195302} }
31. Two-particle quantum interference in tunnel-coupled optical tweezers
    Adam M. Kaufman, Brian J. Lester, Collin M. Reynolds, Michael L. Wall, Michael Foss-Feig, Kaden R. A. Hazzard, Ana Maria Rey, and Cindy A. Regal
    Science 345, 306 (2014) (arXiv:1312.7182, pdf)
    
    In the News
    "Quantum systems under control", Science Perspective
    "The little shop of atoms", JILA Research Highlight
    
    Summary

    The quantum statistics of atoms is typically observed in the behavior of an ensemble via macroscopic observables. However, quantum statistics modifies the behavior of even two particles. Here, we demonstrate near-complete control over all the internal and external degrees of freedom of two laser-cooled 87Rb atoms trapped in two optical tweezers. This controllability allows us to observe signatures of indistinguishability via two-particle interference. Our work establishes laser-cooled atoms in optical tweezers as a promising route to bottom-up engineering of scalable, low-entropy quantum systems.
    Bibtex

    @article{kaufman:two-particle_2014, author = {Kaufman, A. M. and Lester, B. J. and Reynolds, C. M. and Wall, M. L. and Foss-Feig, M. and Hazzard, K. R. A. and Rey, A. M. and Regal, C. A.}, title = {Two-particle quantum interference in tunnel-coupled optical tweezers}, volume = {345}, number = {6194}, pages = {306-309}, year = {2014}, doi = {10.1126/science.1250057}, abstract ={The quantum statistics of atoms is typically observed in the behavior of an ensemble via macroscopic observables. However, quantum statistics modifies the behavior of even two particles. Here, we demonstrate near-complete control over all the internal and external degrees of freedom of two laser-cooled 87Rb atoms trapped in two optical tweezers. This controllability allows us to observe signatures of indistinguishability via two-particle interference. Our work establishes laser-cooled atoms in optical tweezers as a promising route to bottom-up engineering of scalable, low-entropy quantum systems.}, URL = {http://www.sciencemag.org/content/345/6194/306.abstract}, eprint = {http://www.sciencemag.org/content/345/6194/306.full.pdf}, journal = {Science} }
30. 

    Suppressing the loss of ultracold molecules via the continuous quantum Zeno effect
    Bihui Zhu, Bryce Gadway, Michael Foss-Feig, Johannes Schachenmayer, Michael L. Wall, Kaden R. A. Hazzard, Bo Yan, Steven A. Moses, Jacob P. Covey, Deborah S. Jin, Jun Ye, Murray Holland, and Ana Maria Rey
    Physical Review Letters 112, 070404 (2014) ["Editor's Suggestion"]
    (arXiv:1310.2221, pdf)
    In the News: "Dealing with loss", JILA Research Highlight
    

    Summary

    We investigate theoretically the suppression of two-body losses when the on-site loss rate is larger than all other energy scales in a lattice. This work quantitatively explains the recently observed suppression of chemical reactions between two rotational states of fermionic KRb molecules confined in one-dimensional tubes with a weak lattice along the tubes [Yan et al., Nature (London) 501, 521 (2013)]. New loss rate measurements performed for different lattice parameters but under controlled initial conditions allow us to show that the loss suppression is a consequence of the combined effects of lattice confinement and the continuous quantum Zeno effect. A key finding, relevant for generic strongly reactive systems, is that while a single-band theory can qualitatively describe the data, a quantitative analysis must include multiband effects. Accounting for these effects reduces the inferred molecule filling fraction by a factor of 5. A rate equation can describe much of the data, but to properly reproduce the loss dynamics with a fixed filling fraction for all lattice parameters we develop a mean-field model and benchmark it with numerically exact time-dependent density matrix renormalization group calculations.

    Bibtex

    @article{PhysRevLett.112.070404, title = {Suppressing the Loss of Ultracold Molecules Via the Continuous Quantum Zeno Effect}, author = {Zhu, B. and Gadway, B. and Foss-Feig, M. and Schachenmayer, J. and Wall, M.\,L. and Hazzard, K.\,R.\,A. and Yan, B. and Moses, S.\,A. and Covey, J.\,P. and Jin, D.\,S. and Ye, J. and Holland, M. and Rey, A.\,M.}, journal = {Phys. Rev. Lett.}, volume = {112}, issue = {7}, pages = {070404}, numpages = {5}, year = {2014}, month = {Feb}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.112.070404}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.112.070404} }
29. Quenching to unitarity: Quantum dynamics in a 3D Bose gas
    Andrew G. Sykes, John P. Corson, Jose P. D'Incao, Andrew P. Koller, Chris H. Greene, Ana Maria Rey, Kaden R. A. Hazzard, and John L. Bohn
    Physical Review A 89, 021601(R) (2014) (arXiv:1309.0828, pdf)
    
    Summary

    We study the dynamics of a zero-temperature Bose condensate following a sudden quench of the scattering length from noninteracting to unitarity (infinite scattering length). We apply three complementary approaches to understand the momentum distribution and loss rate. First, using a time-dependent variational ansatz for the many-body state, we calculate the dynamics of the momentum distribution. Second, we demonstrate that, at short times and large momenta compared to those set by the density, the physics can be understood within a simple, analytic two-body model. We make a quantitative prediction for the evolution of Tan's contact and find features in the momentum distribution that are absent in equilibrium. Third, we study three-body loss at finite density under the same dynamic scenario. We find lifetimes that are long compared to the saturation times of large-momentum modes, and we relate this result to the three-body inelasticity parameter.
    Bibtex

    @ARTICLE{sykes:quenching_2013, title = {Quenching to unitarity: Quantum dynamics in a three-dimensional Bose gas}, author = {Sykes, A. G. and Corson, J. P. and D'Incao, J. P. and Koller, A. P. and Greene, C. H. and Rey, A. M. and Hazzard, K. R. A. and Bohn, J. L.}, journal = {Phys. Rev. A}, volume = {89}, issue = {2}, pages = {021601}, numpages = {5}, year = {2014}, month = {Feb}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.89.021601}, url = {http://link.aps.org/doi/10.1103/PhysRevA.89.021601} }
28. Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence
    Michael Foss-Feig, Kaden R. A. Hazzard, John J. Bollinger, Ana Maria Rey, and Charles W. Clark
    New Journal of Physics 15, 113008 (2013) (arXiv:1306.0172, pdf)
    Chosen as "IOP Select" article
    
    Summary

    Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms realize long-ranged Ising models, which even in the absence of a transverse field can give rise to highly non-classical dynamics and long-range quantum correlations. In the first part of this paper, we present a detailed theoretical framework for studying the dynamics of such systems driven (at time t=0) into arbitrary unentangled non-equilibrium states, thus greatly extending and unifying the work of Ref. [1]. Specifically, we derive exact expressions for closed-time-path ordered correlation functions, and use these to study experimentally relevant observables, e.g. Bloch vector and spin-squeezing dynamics. In the second part, these correlation functions are then used to derive closed-form expressions for the dynamics of arbitrary spin-spin correlation functions in the presence of both T_1 (spontaneous spin relaxation/excitation) and T_2 (dephasing) type decoherence processes. Even though the decoherence is local, our solution reveals that the competition between Ising dynamics and T_1 decoherence gives rise to an emergent non-local dephasing effect, thereby drastically amplifying the degradation of quantum correlations. In addition to identifying the mechanism of this deleterious effect, our solution points toward a scheme to eliminate it via measurement-based coherent feedback.
    Bibtex

    @article{foss-feig:dynamical_2013, author={M Foss-Feig and K R A Hazzard and J J Bollinger and A M Rey and C W Clark}, title={Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence}, journal={New Journal of Physics}, volume={15}, number={11}, pages={113008}, url={http://stacks.iop.org/1367-2630/15/i=11/a=113008}, year={2013}}
27. Observation of dipolar spin-exchange interactions with lattice-confined polar molecules
    Bo Yan, Steven A. Moses, Bryce Gadway, Jacob P. Covey, Kaden R. A. Hazzard, Ana Maria Rey, Deborah S. Jin, and Jun Ye
    Nature 501, 521 (2013) (arXiv:1305.5598, pdf)
    In the News
    "Molecules line up in laser grid", Physics World
    "Rotating molecules as quantum magnets", Nature News and Views
    "Spins swapped at a distance", Overclocker's club
    "The great spin swap", JILA Research Highlight
    "Beyond quantum simulation: JILA physicists create 'crystal' of spin-swapping ultracold gas molecules", NIST Newsletter
    (also on phys.org, ScienceDaily, Nanotechnology News, pro-physik.de...)
    Summary

    In a step towards developing a system in which to study quantum magnetism, the long-range dipolar interactions of polar molecules pinned in a three-dimensional optical lattice are used to realize a lattice spin model.
    Bibtex

    @ARTICLE{yan:realizing_2013, author = {Yan, Bo and Moses, Steven A. and Gadway, Bryce and Covey, Jacob P. and Hazzard, Kaden R. A. and Rey, Ana Maria and Jin, Deborah S. and Ye, Jun}, title = {Observation of dipolar spin-exchange interactions with lattice-confined polar molecules}, journal = {Nature}, year = {2013}, volume = {501}, pages = {521}, number = {7468}, month = sep, issn = {0028-0836}, url = {http://dx.doi.org/10.1038/nature12483} }
26. Kitaev honeycomb and other exotic spin models with polar molecules
    Alexey V. Gorshkov, Kaden R. A. Hazzard, and Ana Maria Rey
    Molecular Physics 111, 1908 (2013), invited article for Bretislav Friedrich special issue (arXiv:1301.5636, pdf)
    
    Summary

    We show that ultracold polar molecules pinned in an optical lattice can be used to access a variety of exotic spin models, including the Kitaev honeycomb model. Treating each molecule as a rigid rotor, we use DC electric and microwave fields to define superpositions of rotational levels as effective spin degrees of freedom, while dipole-dipole interactions give rise to interactions between the spins. In particular, we show that, with sufficient microwave control, the interaction between two spins can be written as a sum of five independently controllable Hamiltonian terms proportional to the five rank-2 spherical harmonics Y_{2,q}(theta,phi), where (theta,phi) are the spherical coordinates of the vector connecting the two molecules. To demonstrate the potential of this approach beyond the simplest examples studied in [S. R. Manmana et al., arXiv:1210.5518v2], we focus on the realization of the Kitaev honeycomb model, which can support exotic non-Abelian anyonic excitations. We also discuss the possibility of generating spin Hamiltonians with arbitrary spin S, including those exhibiting SU(N=2S+1) symmetry.
    Bibtex

    @ARTICLE{gorshkov:kitaev_2013, author = {Gorshkov, Alexey V. and Hazzard, Kaden R. A. and Rey, Ana Maria}, title = {Kitaev honeycomb and other exotic spin models with polar molecules}, journal = {Molecular Physics}, year = {2013}, volume = {111}, pages = {1908-1916}, number = {12-13}, doi = {10.1080/00268976.2013.800604} }
25. Nonequilibrium dynamics of arbitrary-range Ising models with decoherence: An exact analytic solution
    Michael Foss-Feig, Kaden R.A. Hazzard, John J. Bollinger, and Ana Maria Rey
    Physical Review A 87, 042101 (2013) (arxiv:1209.5795, pdf)
    
    Summary

    The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics. In a step toward understanding this interplay, we obtain an exact analytic solution for the nonequilibrium dynamics of Ising models with arbitrary couplings (and therefore in arbitrary dimension) and subject to local Markovian decoherence. Our solution shows that decoherence significantly degrades the nonclassical correlations developed during coherent Ising spin dynamics, which relax much faster than predicted by treating decoherence and interactions separately. We also show that the competition of decoherence and interactions induces a transition from oscillatory to overdamped dynamics that is absent at the single-particle or mean-field level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems. In particular, we apply our results to the NIST Penning trapped-ion experiment and show that the current experiment is capable of producing entanglement amongst hundreds of quantum spins.
    Bibtex

    @article{PhysRevA.87.042101, title = {Nonequilibrium dynamics of arbitrary-range Ising models with decoherence: An exact analytic solution}, author = {Foss-Feig, Michael and Hazzard, Kaden R. A. and Bollinger, John J. and Rey, Ana Maria}, journal = {Phys. Rev. A}, volume = {87}, issue = {4}, pages = {042101}, numpages = {8}, year = {2013}, month = {Apr}, doi = {10.1103/PhysRevA.87.042101}, url = {http://link.aps.org/doi/10.1103/PhysRevA.87.042101}, publisher = {American Physical Society} }
24. Topological phases in ultracold polar-molecule quantum magnets
    Salvatore R. Manmana, E. M. Stoudenmire, Kaden R. A. Hazzard, Ana Maria Rey, and Alexey V. Gorshkov
    Physical Review B 87, 081106(R) (2013) (arxiv:1210.5518, pdf)
    
    Summary

    We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin S ≥ 1/2 and with interactions featuring a direction-dependent spin anisotropy. This is achieved by encoding the effective spin degrees of freedom in microwave-dressed rotational states of the molecules and by coupling the spins through dipolar interactions. We demonstrate how one of the experimentally most accessible anisotropies stabilizes symmetry protected topological phases in spin ladders. Using the numerically exact density matrix renormalization group method, we find that these interacting phases—previously studied only in the nearest-neighbor case—survive in the presence of long-range dipolar interactions. We also show how to use our approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb models. Experimental detection schemes and imperfections are discussed.
    Bibtex

    @ARTICLE{manmana:topological-phases_2012, title = {Topological phases in ultracold polar-molecule quantum magnets}, author = {Manmana, Salvatore R. and Stoudenmire, E. M. and Hazzard, Kaden R. A. and Rey, Ana Maria and Gorshkov, Alexey V.}, journal = {Phys. Rev. B}, volume = {87}, issue = {8}, pages = {081106}, numpages = {6}, year = {2013}, month = {Feb}, doi = {10.1103/PhysRevB.87.081106}, url = {http://link.aps.org/doi/10.1103/PhysRevB.87.081106}, publisher = {American Physical Society} }
23. Far-from-Equilibrium Quantum Magnetism with Ultracold Polar Molecules
    Kaden R.A. Hazzard, Salvatore R. Manmana, Michael Foss-Feig, and Ana Maria Rey
    Physical Review Letters 110, 075301 (2013) (arXiv:1209.4076, pdf)
    In the News: "Model Behavior", JILA Research Highlight
    
    Summary

    Recent theory has indicated how to emulate tunable models of quantum magnetism with ultracold polar molecules. Here we show that present molecule optical lattice experiments can accomplish three crucial goals for quantum emulation, despite currently being well below unit filling and not quantum degenerate. The first is to verify and benchmark the models proposed to describe these systems. The second is to prepare correlated and possibly useful states in well-understood regimes. The third is to explore many-body physics inaccessible to existing theoretical techniques. Our proposal relies on a nonequilibrium protocol that can be viewed either as Ramsey spectroscopy or an interaction quench. The proposal uses only routine experimental tools available in any ultracold molecule experiment. To obtain a global understanding of the behavior, we treat short times pertubatively, develop analytic techniques to treat the Ising interaction limit, and apply a time-dependent density matrix renormalization group to disordered systems with long range interactions.
    Bibtex

    @ARTICLE{hazzard:far_2012, title = {Far-from-Equilibrium Quantum Magnetism with Ultracold Polar Molecules}, author = {Hazzard, Kaden R. A. and Manmana, Salvatore R. and Foss-Feig, Michael and Rey, Ana Maria}, journal = {Phys. Rev. Lett.}, volume = {110}, issue = {7}, pages = {075301}, numpages = {6}, year = {2013}, month = {Feb}, doi = {10.1103/PhysRevLett.110.075301}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.110.075301}, publisher = {American Physical Society} }
22. Universality class of quantum criticality in the two-dimensional Hubbard model at intermediate temperatures (t^2/U << T << t)
    Kaden R.A. Hazzard, Ana Maria Rey, and Richard T. Scalettar
    Physical Review B 87, 035110 (2013) (arxiv:1106.2330, pdf)
    
    Summary

    By using numerically exact determinantal Monte Carlo we show that the dilute Fermi gas quantum critical theory quantitatively describes the behavior of the density and compressibility along the Mott/metal crossover in the two-dimensional Hubbard model for temperatures somewhat less than (roughly half) the tunneling but greater than (roughly twice) the superexchange energy. In contrast, we find that other observables such as the kinetic energy, doubly occupied sites, and magnetization in a finite Zeeman field are poorly described by the same dilute Fermi gas universality class. In addition to these findings’ fundamental interest, they are relevant to cold atom systems, where the intermediate temperature regime is currently in experimental reach.
    Bibtex

    @article{hazzard:universality_2013, title = {Universality class of quantum criticality in the two-dimensional Hubbard model at intermediate temperatures (${t}^{2}/U$\ll${}T$\ll${}t$)}, author = {Hazzard, Kaden R. A. and Rey, Ana Maria and Scalettar, Richard T.}, journal = {Phys. Rev. B}, volume = {87}, issue = {3}, pages = {035110}, numpages = {7}, year = {2013}, month = {Jan}, doi = {10.1103/PhysRevB.87.035110}, url = {http://link.aps.org/doi/10.1103/PhysRevB.87.035110}, publisher = {American Physical Society} }
21. Adiabatic Loading of One-Dimensional SU(N) Alkaline-Earth-Atom Fermions in Optical Lattices
    Lars Bonnes, Kaden R.A. Hazzard, Salvatore R. Manmana, Ana Maria Rey, and Stefan Wessel
    Physical Review Letters 109, 205305 (2012) (arxiv:1207.3900, pdf)
    
    Summary

    Ultracold fermionic alkaline earth atoms confined in optical lattices realize Hubbard models with internal SU(N) symmetries, where N can be as large as ten. Such systems are expected to harbor exotic magnetic physics at temperatures below the superexchange energy scale. Employing quantum Monte Carlo simulations to access the low-temperature regime of one-dimensional chains, we show that after adiabatically loading a weakly interacting gas into the strongly interacting regime of an optical lattice, the final temperature decreases with increasing N. Furthermore, we estimate the temperature scale required to probe correlations associated with low-temperature SU(N) magnetism. Our findings are encouraging for the exploration of exotic large-N magnetic states in ongoing experiments.
    Bibtex

    @article{hazzard:adiabatic_2012, title = {Adiabatic Loading of One-Dimensional $\mathrm{SU}(N)$ Alkaline-Earth-Atom Fermions in Optical Lattices}, author = {Bonnes, Lars and Hazzard, Kaden R. A. and Manmana, Salvatore R. and Rey, Ana Maria and Wessel, Stefan}, journal = {Phys. Rev. Lett.}, volume = {109}, issue = {20}, pages = {205305}, numpages = {5}, year = {2012}, month = {Nov}, doi = {10.1103/PhysRevLett.109.205305}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.109.205305}, publisher = {American Physical Society} }
20. High-temperature properties of fermionic alkaline-earth-metal atoms in optical lattices
    Kaden R.A. Hazzard, Victor Gurarie, Michael Hermele, and Ana Maria Rey
    Physical Review A 85, 041604(R) (2012) (arxiv:1011.0032, pdf)
    In the News: "New Flavors of Quantum Magnetism", JILA Research Highlight
    
    Summary

    We calculate experimentally relevant properties of trapped fermionic alkaline-earth-metal atoms in an optical lattice, modeled by the SU(N) Hubbard model. We employ a high-temperature expansion that is accurate when the temperature is larger than the tunneling rate, similar to current regimes in ultracold atom experiments. In addition to exploring the Mott insulator-metal crossover, we calculate final temperatures achieved by the standard experimental protocol of adiabatically ramping from a noninteracting gas, as a function of initial gas temperature. Of particular experimental interest, we find that increasing N for fixed particle numbers and initial temperatures gives substantially colder Mott insulators after the adiabatic ramping, up to more than a factor of 5 for relevant parameters. This cooling happens for all N, fixing the initial entropy, or for all N≲20 (the exact value depends on dimensionality), at fixed, experimentally relevant initial temperatures.
    Bibtex

    @ARTICLE{hazzard:high-temperature_2012, title = {High-temperature properties of fermionic alkaline-earth-metal atoms in optical lattices}, author = {Hazzard, Kaden R. A. and Gurarie, Victor and Hermele, Michael and Rey, Ana Maria}, journal = {Phys. Rev. A}, volume = {85}, issue = {4}, pages = {041604}, numpages = {5}, year = {2012}, month = {Apr}, doi = {10.1103/PhysRevA.85.041604}, url = {http://link.aps.org/doi/10.1103/PhysRevA.85.041604}, publisher = {American Physical Society} }
19. SU(N) magnetism in chains of ultracold alkaline earth atoms: Mott transitions and quantum correlations
    Salvatore R. Manmana, Kaden R.A. Hazzard, Gang Chen, Adrian E. Feiguin, and Ana Maria Rey
    Physical Review A 84, 043601 (2011) (arxiv:1108.2327, pdf)
    
    Summary

    We investigate one dimensional SU$(N)$ Hubbard chains at zero temperature, which can be emulated with ultracold alkaline earth atoms, by using the density matrix renormalization group (DMRG), Bethe ansatz (BA), and bosonization. We compute experimental observables and use the DMRG to benchmark the accuracy of the Bethe ansatz for $N> 2$ where the BA is only approximate. In the worst case, we find a relative error $\epsilon \lesssim 4%$ in the BA ground state energy for $N \leq 4$ at filling 1/N, which is due to the fact that BA improperly treats the triply and higher occupied states. Using the DMRG for $N \leq 4$ and the BA for large $N$, we determine the regimes of validity of strong- and weak-coupling perturbation theory for all values of $N$ and in particular, the parameter range in which the system is well described by a SU(N) Heisenberg model at filling 1/N. We find this depends only weakly on $N$. We investigate the Berezinskii-Kosterlitz-Thouless phase transition from a Luttinger liquid to a Mott-insulator by computing the fidelity susceptibility and the Luttinger parameter $K_\rho$ at 1/N filling. The numerical findings give strong evidence that the fidelity susceptibility develops a minimum at a critical interaction strength which is found to occur at a finite positive value for $N> 2$.
    Bibtex

    @ARTICLE{manmana:sun-magnetism_2011, title = {SU$(N)$ magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations}, month = {Oct}, journal = {Phys. Rev. A}, doi = {10.1103/PhysRevA.84.043601}, author = {Manmana, Salvatore R. and Hazzard, Kaden R. A. and Chen, Gang and Feiguin, Adrian E. and Rey, Ana Maria}, year = {2011}, issue = {4}, url = {http://link.aps.org/doi/10.1103/PhysRevA.84.043601}, numpages = {17}, publisher = {American Physical Society}, pages = {043601}, volume = {84} }
18. Spectroscopy of dipolar fermions in 2D pancakes and 3D lattices
    Kaden R.A. Hazzard, Alexey V. Gorshkov, and Ana Maria Rey
    Physical Review A 84, 033608 (2011) (arxiv:1106.1718, pdf)
    
    Summary

    Motivated by ongoing measurements at JILA, we calculate the recoil-free spectra of dipolar interacting fermions, for example ultracold heteronuclear molecules, in a one-dimensional lattice of two-dimensional pancakes, spectroscopically probing transitions between different internal (e.g., rotational) states. We additionally incorporate $p$-wave interactions and losses, which are important for reactive molecules such as KRb. Moreover, we consider other sources of spectral broadening: interaction-induced quasiparticle lifetimes and the different polarizabilities of the different rotational states used for the spectroscopy. Although our main focus is molecules, some of the calculations are also useful for optical lattice atomic clocks. For example, understanding the $p$-wave shifts between identical fermions and small dipolar interactions coming from the excited clock state are necessary to reach future precision goals. Finally, we consider the spectra in a deep 3D lattice and show how they give a great deal of information about static correlation functions, including \textit{all} the moments of the density correlations between nearby sites. The range of correlations measurable depends on spectroscopic resolution and the dipole moment.
    Bibtex

    @article{hazzard:spectroscopy, journal = {Phys. Rev. A}, month = {Sep}, url = {http://link.aps.org/doi/10.1103/PhysRevA.84.033608}, publisher = {American Physical Society}, author = {Hazzard, Kaden R. A. and Gorshkov, Alexey V. and Rey, Ana Maria}, title = {Spectroscopy of dipolar fermions in layered two-dimensional and three-dimensional lattices}, year = {2011}, pages = {033608}, numpages = {13}, volume = {84}, doi = {10.1103/PhysRevA.84.033608}, issue = {3} }
17. Techniques to measure quantum criticality in cold atoms
    Kaden R.A. Hazzard and Erich J. Mueller
    Physical Review A 84, 013604 (2011) (arXiv:1006.0969, pdf)
    
    Summary

    We describe how rescaling experimental data obtained from cold atom density profiles can reveal signatures of quantum criticality. We identify a number of important questions which can be answered by analyzing experimental data in this manner. We show that such experiments can distinguish different universality classes and that the signatures are robust against temperature, noise, and finite system size.
    Bibtex

    @Article{hazzard_techniques_2011, title = {Techniques to measure quantum criticality in cold atoms}, author = {Hazzard, Kaden R. A. and Mueller, Erich J.}, journal = {Phys. Rev. A}, volume = {84}, number = {1}, pages = {013604}, numpages = {10}, year = {2011}, month = {Jul}, doi = {10.1103/PhysRevA.84.013604}, publisher = {American Physical Society} }
16. Local versus global equilibration near the bosonic Mott-superfluid transition
    Stefan S. Natu, Kaden R.A. Hazzard, and Erich J. Mueller
    Physical Review Letters 106, 125301 (2011) (arxiv:1009.5728, pdf)
    
    Summary

    We study the response of trapped two dimensional cold bosons to time dependent lattices. We find that in lattice ramps from $11$ (superfluid, $\hbar/U_{\text{i}} = 3$ms, $\hbar/J_{\text{i}} = 45$ms) to $16$ recoils (Mott, $\hbar/U_{\text{f}} = 2$ms, $\hbar/J_{\text{f}} = 130$ms) the local number fluctuations remains at their equilibrium values if ramps are slower than $3$ ms. Global transport, however, is much slower ($1$s), especially in the presence of Mott shells. This separation of timescales has practical implications for cold atom experiments and cooling protocols.
    Bibtex

    @ARTICLE{natu:equilibration, author = {Natu, Stefan S. and Hazzard, Kaden R. A. and Mueller, Erich J.}, volume = {106}, journal = {Phys. Rev. Lett.}, month = {Mar}, numpages = {4}, title = {Local Versus Global Equilibration near the Bosonic Mott-Insulator\char21{}Superfluid Transition}, year = {2011}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.106.125301}, doi = {10.1103/PhysRevLett.106.125301}, issue = {12}, publisher = {American Physical Society}, pages = {125301} }
15. 

    Candidate theories to explain the anomalous spectroscopic signatures of atomic H in molecular H$_2$ crystals
    Kaden R.A. Hazzard and Erich J. Mueller
    Physical Review B 82, 014303 (2010) ["Editor's Suggestion"] (arxiv:1004.5577,pdf)
    

    Summary

    We analyze a number of proposed explanations for spectroscopic anomalies observed in atomic hydrogen defects embedded in a solid molecular hydrogen matrix. In particular, we critically evaluate the possibility that these anomalies are related to Bose-Einstein condensation (both global and local). For each proposed mechanism we discuss which aspects of the experiment can be explained, and make predictions for future experiments.

    Bibtex

    @Article{PhysRevB.82.014303, title = {Candidate theories to explain the anomalous spectroscopic signatures of atomic H in molecular $ H_2 $ crystals}, author = {Hazzard, Kaden R. A. and Mueller, Erich J.}, journal = {Phys. Rev. B}, volume = {82}, number = {1}, pages = {014303}, numpages = {6}, year = {2010}, month = {Jul}, doi = {10.1103/PhysRevB.82.014303}, publisher = {American Physical Society} }
14. Radio-frequency spectra of bosons in optical lattices: bimodality due to many body correlations
    Kaden R.A. Hazzard and Erich J. Mueller
    Physical Review A 81, 033404 (2010) (arxiv:0907.1332, pdf).
    
    Summary

    We calculate the radio-frequency spectrum of a trapped cloud of cold bosonic atoms in an optical lattice. By using random phase and local-density approximations we produce both trap-averaged and spatially resolved spectra, identifying simple features in the spectra that reveal information about both superfluidity and correlations. Our approach is exact in the deep Mott limit and in the dilute superfluid when the hopping rates for the two internal spin states are equal. It contains final state interactions, obeys the Ward identities (and the associated conservation laws), and satisfies the f-sum rule. Motivated by earlier work by Sun, Lannert, and Vishveshwara [Phys. Rev. A 79, 043422 (2009)], we also discuss the features that arise in a spin-dependent optical lattice.
    Bibtex

    @Article{PhysRevA.81.033404, title = {Many-body physics in the radio-frequency spectrum of lattice bosons}, author = {Hazzard, Kaden R. A. and Mueller, Erich J.}, journal = {Phys. Rev. A}, volume = {81}, number = {3}, pages = {033404}, numpages = {6}, year = {2010}, month = {Mar}, doi = {10.1103/PhysRevA.81.033404}, publisher = {American Physical Society} }
13. On-site correlations in optical lattices: band mixing to coupled quantum Hall puddles Kaden R.A. Hazzard and Erich J. Mueller
    Physical Review A 81, 031602(R) (2010) (arxiv:0902.4707, pdf).
    
    Summary

    We extend the standard Bose-Hubbard model to capture arbitrarily strong on-site correlations. In addition to being important for quantitatively modeling experiments, for example, with Rubidium atoms, these correlations must be included to describe more exotic situations. Two such examples are when the interactions are made large via a Feshbach resonance, or when each site rotates rapidly, making a coupled array of quantum Hall puddles. Remarkably, even the mean field approximation to our model includes all on-site correlations. We describe how these on-site correlations manifest themselves in the system's global properties: modifying the phase diagram and depleting the condensate.
    Bibtex

    @Article{PhysRevA.81.031602, title = {On-site correlations in optical lattices: Band mixing to coupled quantum Hall puddles}, author = {Hazzard, Kaden R. A. and Mueller, Erich J.}, journal = {Phys. Rev. A}, volume = {81}, number = {3}, pages = {031602}, numpages = {4}, year = {2010}, month = {Mar}, doi = {10.1103/PhysRevA.81.031602}, publisher = {American Physical Society} }
12. Stirring trapped atoms into Fractional Quantum Hall puddles
    Stefan K. Baur, Kaden R.A. Hazzard, and Erich J. Mueller (KRAH and SKB co-first authors)
    Physical Review A 78, 061608(R) (2008) (arXiv:0806.1517, pdf)
    
    Summary

    We theoretically explore the generation of few-body analogs of fractional quantum Hall states. We consider an array of identical few-atom clusters (n=2,3,4), each cluster trapped at the node of an optical lattice. By temporally varying the amplitude and phase of the trapping lasers, one can introduce a rotating deformation at each site. We analyze protocols for coherently transferring ground-state clusters into highly correlated states, producing theoretical fidelities (probability of reaching the target state) in excess of 99%.
    Bibtex

    @article{baur:061608, author = {Stefan K. Baur and Kaden R. A. Hazzard and Erich J. Mueller}, collaboration = {}, title = {Stirring trapped atoms into fractional quantum Hall puddles}, publisher = {APS}, year = {2008}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {78}, number = {6}, eid = {061608}, numpages = {4}, pages = {061608}, keywords = {ground states; optical lattices; probability; quantum Hall effect; strongly correlated electron systems}, url = {http://link.aps.org/abstract/PRA/v78/e061608}, doi = {10.1103/PhysRevA.78.061608} }
11. Influence of film-mediated interactions on the microwave and radio spectrum of spin-polarized hydrogen on helium films
    Kaden R.A. Hazzard and Erich J. Mueller
    Physical Review Letters 101, 165301 (2008) (arxiv:0804.1543, pdf)
    
    Summary

    We argue that helium film-mediated hydrogen-hydrogen interactions strongly reduce the magnitude of cold collision shifts in spin-polarized hydrogen adsorbed on a helium film. With plausible assumptions about experimental parameters this can explain (i) the 2 orders of magnitude discrepancy between previous theory and recent experiments and (ii) the anomalous dependence of the cold collision frequency shifts on the film's 3He covering. The mediated interaction is attractive, suggesting that in current experiments the gas will become unstable before reaching the Kosterlitz-Thouless transition.
    Bibtex

    @article{hazzard:165301, author = {Kaden R. A. Hazzard and Erich J. Mueller}, collaboration = {}, title = {Influence of Film-Mediated Interactions on the Microwave and Radio Frequency Spectrum of Spin-Polarized Hydrogen on Helium Films}, publisher = {APS}, year = {2008}, journal = {Physical Review Letters}, volume = {101}, number = {16}, eid = {165301}, numpages = {4}, pages = {165301}, url = {http://link.aps.org/abstract/PRL/v101/e165301}, doi = {10.1103/PhysRevLett.101. 165301} }
10. Hyperfine spectra of trapped bosons in optical lattices
    Kaden R.A. Hazzard and Erich J. Mueller
    Physical Review A 76, 063612 (2007) (arxiv:0708.3657, pdf)
    
    Summary

    We calculate the interaction induced inhomogeneous broadening of spectral lines in a trapped Bose gas as a function of the depth of a three-dimensional cubic optical lattice. As observed in recent experiments, we find that the terraced "wedding-cake" structure of Mott plateaus splits the spectrum into a series of discrete peaks. The spectra are extremely sensitive to density corrugations and trap anharmonicities. For example, even when the majority of the cloud is superfluid the spectrum displays discrete peaks.
    Bibtex

    @article{hazzard:063612, author = {Kaden R. A. Hazzard and Erich J. Mueller}, collaboration = {}, title = {Hyperfine spectra of trapped bosons in optical lattices}, publisher = {APS}, year = {2007}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {76}, number = {6}, eid = {063612}, numpages = {7}, pages = {063612}, keywords = {boson systems; hyperfine structure; optical lattices; quantum optics; radiation pressure; spectral line broadening}, url = {http://link.aps.org/abstract/PRA/v76/e063612}, doi = {10.1103/PhysRevA.76.063612} }
9. Fast Diffusion Mechanism of Silicon Tri-interstitial Defects
   Yaojun A. Du, Stephen A. Barr, Kaden R.A. Hazzard, Thomas J. Lenosky, Richard G. Hennig, and John W. Wilkins 
   Physical Review B 72, 241306(R) (2005), (arxiv:cond-mat/0503473, pdf)
   
   Summary

   Molecular dynamics combined with the nudged elastic band method reveals the microscopic self-diffusion process of compact silicon tri-interstitials. Tight-binding molecular dynamics paired with ab initio density functional calculations speed the identification of diffusion mechanisms. The diffusion pathway can be visualized as a five defect-atom object both translating and rotating in a screwlike motion along <111> directions. The density functional theory yields a diffusion constant of $4 \times 10^{–5} \exp(–0.49 eV/kBT) cm^2/s$. The low diffusion barrier of the compact tri-interstitial may be important in the growth of ion-implantation-induced extended interstitial defects.
   Bibtex

   @article{du:241306, author = {Yaojun A. Du and Stephen A. Barr and Kaden R. A. Hazzard and Thomas J. Lenosky and Richard G. Hennig and John W. Wilkins}, collaboration = {}, title = {Fast diffusion mechanism of silicon tri-interstitial defects}, publisher = {APS}, year = {2005}, journal = {Physical Review B (Condensed Matter and Materials Physics)}, volume = {72}, number = {24}, eid = {241306}, numpages = {4}, pages = {241306}, keywords = {silicon; elemental semiconductors; interstitials; self-diffusion; molecular dynamics method; tight-binding calculations; ab initio calculations; density functional theory}, url = {http://link.aps.org/abstract/PRB/v72/e241306}, doi = {10.1103/PhysRevB.72. 241306} }
8. A Novel Dielectric Anomaly in Cuprates and Nickelates: Signature of an Electronic Glassy State
   Tuson Park, Z. Nussinov, Kaden R.A. Hazzard, V.A. Sidorov, A.V. Balatsky, J.L. Sarrao, S.-W. Cheong, M.F. Hundley, J.-S. Lee, Q. Jia, and J.D. Thompson
   Physical Review Letters 94, 017002 (2005) (arxiv:cond-mat/0404446, pdf)
   
   Summary

   The low-frequency dielectric response of hole-doped insulators La$_2$Cu$_{1-x}$Li$_x$O_4 and La$_{2-x}$Sr$_x$NiO$_4$ shows a large dielectric constant $\epsilon'$ at high temperature and a steplike drop by a factor of 100 at a material-dependent low temperature $T_f$. $T_f$ increases with frequency, and the dielectric response shows universal scaling in a Cole-Cole plot, suggesting that a charge-glass state is realized both in the cuprates and in the nickelates.
   Bibtex

   @article{park:017002, author = {Tuson Park and Z. Nussinov and K. R. A. Hazzard and V. A. Sidorov and A. V. Balatsky and J. L. Sarrao and S.-W. Cheong and M. F. Hundley and Jang-Sik Lee and Q. X. Jia and J. D. Thompson}, collaboration = {}, title = {Novel Dielectric Anomaly in the Hole-Doped La$_2$Cu$_{1-x}$Li_$x$O$_4$ and La$_{2-x}$Sr$_x$NiO$_4$ Insulators: Signature of an Electronic Glassy State}, publisher = {APS}, year = {2005}, journal = {Physical Review Letters}, volume = {94}, number = {1}, eid = {017002}, numpages = {4}, pages = {017002}, keywords = {lanthanum compounds; copper compounds; strontium compounds; permittivity; dielectric relaxation}, url = {http://link.aps.org/abstract/PRL/v94/e017002}, doi = {10.1103/PhysRevLett.94. 017002} }
7. Complexity of Small Silicon Self-interstitial Clusters
   D.A. Richie, Jeongnim Kim, Stephen A. Barr, Kaden R.A. Hazzard, Richard Hennig, and John W. Wilkins
   Physical Review Letters 92, 045501 (2004) (pdf)
   In the news: "Salted Away Silicon", NCSA News
   
   Summary

   The combination of long-time, tight-binding molecular dynamics and real-time multiresolution analysis techniques reveals the complexity of small silicon interstitial defects. The stability of identified structures is confirmed by ab initio relaxations. The majority of structures were previously unknown, demonstrating the effectiveness of the approach. A new, spatially extended tri-interstitial ground state structure is identified as a probable nucleation site for larger extended defects and may be key for the compact-to-extended transition.
   Bibtex

   @article{richie:045501, author = {D. A. Richie and Jeongnim Kim and Stephen A. Barr and Kaden R. A. Hazzard and Richard Hennig and John W. Wilkins}, collaboration = {}, title = {Complexity of Small Silicon Self-Interstitial Defects}, publisher = {APS}, year = {2004}, journal = {Physical Review Letters}, volume = {92}, number = {4}, eid = {045501}, numpages = {4}, pages = {045501}, keywords = {silicon; interstitials; molecular dynamics method; ab initio calculations; tight-binding calculations; defect states; elemental semiconductors}, url = {http://link.aps.org/abstract/PRL/v92/e045501}, doi = {10.1103/PhysRevLett.92. 045501} }

Proceedings and other refereed publications with results unavailable elsewhere

6. Detection and Visualization of Anomalous Structures in Molecular Dynamics Data
   Sameep Mehta, Raghu Machiraju, Srini Parthasarathy, Kaden R.A. Hazzard, and John Wilkins
   IEEE Visualization, Proceedings of the conference on Visualization '04, 465-472 (2004) (pdf)
   
   Summary

   In this article we explore techniques to detect and visualize features in data from molecular dynamics (MD) simulations. Although the techniques proposed are general, we focus on silicon (Si) atomic systems. The first set of methods use 3D location of atoms. Defects are detected and categorized using local operators and statistical modeling. Our second set of exploratory techniques employ electron density data. This data is visualized to glean the defects. We describe techniques to automatically detect the salient iso-values for iso-surface extraction and designing transfer functions. We compare and contrast the results obtained from both sources of data. Essentially, we find that the methods of defect (feature) detection are at least as robust as those based on the exploration of electron density for Si systems.
   Bibtex

   @inproceedings{1034481, author = {Mehta,, Sameep and Hazzard,, Kaden and Machiraju,, Raghu and Parthasarathy,, Srinivasan and Wilkins,, John}, title = {Detection and Visualization of Anomalous Structures in Molecular Dynamics Simulation Data}, booktitle = {VIS '04: Proceedings of the conference on Visualization '04}, year = {2004}, isbn = {0-7803-8788-0}, pages = {465--472}, doi = {http://dx.doi.org/10.1109/VIS.2004.23}, publisher = {IEEE Computer Society}, address = {Washington, DC, USA}, }
5. Mining Temporally-Varying Phenomena in Scientific Datasets
   R. Machiraju, S. Parthasarathy, J. Wilkins, D. Thompson, B. Gatlin, D. Richie, T. Choy, M. Jiang, S. Mehta, M. Coatney, S. Barr, and Kaden R.A. Hazzard
   Advances in Knowledge Discovery, 2003, eds. H. Kargupta et al. (pdf)
   
   Summary

   Simulation is enhancing and, in many instances, replacing experimentation as a means to gain insight into complex physical phenomena. Recent advances in computer hardware and numerical methods have made it possible to simulate physical phenomena at very fine temporal and spatial resolutions. Unfortunately, given the enormous sizes of the datasets involved, analyzing datasets produced by these simulations is extremely challenging. In order to more fully exploit simulation, the analysis of these large datasets must advance beyond current techniques that are based on interactive visualization.

   We outline our vision for one such approach and describe progress on a unified framework that promises to provide a novel method to explore large simulation data sets. We illustrate its application to two disparate science drivers – temporally varying solid and fluid systems. In both applications, there are hidden hierarchies of features as well as many abstract multidimensional feature characterizations (e.g. shapes). Through this framework, we offer a systematic approach to detect, characterize, and track meta-stable features as well as formulate hypotheses about their evolution – an important step in extracting vital information from such complex systems.

   Bibtex

   @INCOLLECTION{ machiraju:data-mining-science, author = {R. Machiraju and S. Parthasarathy and J. Wilkins and D. Thompson and B. Gatlin and D. Richie and T. Choy and M. Jiang and S. Mehta and M. Coatney and S. Barr and Kaden R.A. Hazzard}, title = {Mining Temporally-Varying Phenomena in Scientific Datasets}, booktitle = {Data Mining: Next Generation Challenges and Future Directions}, publisher = {AAAI Press}, year = {2003} }
4. Molecular dynamics as a bridge: fundamentals, methods, and current research
   Kaden R. A. Hazzard
   Reviews in Undergraduate Research, vol. 1, issue 2, 2003 (pdf)
   
   Summary

   In short, this article explain why molecular dynamics is useful and where it has been used, it gives the fundamentals necessary for understanding a MD simulation, and discusses research into MD methods themselves, namely Voter et al.'s acceleration methods.

   Bibtex

   @ARTICLE{hazzard:md-review, author = {Kaden R.A. Hazzard}, title = {Molecular dynamics as a bridge: fundamentals, methods, and current research}, journal = {Catalyst: reviews in undergraduate research}, year = {2003}, volume = {2} }
3. Feature Mining Algorithms for Scientific Data
   M. Jiang, T.-S. Choy, S. Mehta, M. Coatney, S. Barr, Kaden R.A. Hazzard, D. Richie, S. Parthasarathy, R. Machiraju, David Thompson, J. Wilkins, and Boyd Gaytlin
   Proceedings of SIAM Data Mining Conference, edited by D. Barbara and C. Kamath, May 2003, 13-24. (pdf)
   
   Summary

   Numerical simulation is replacing experimentation as a means to gain insight into complex physical phenom- ena. Analyzing the data produced by such simulations is extremely challenging, given the enormous sizes of the datasets involved. In order to make efficient progress, analyzing such data must advance from current techniques that only visualize static images of the data, to novel techniques that can mine, track, and visualize the important features in the data. In this paper, we present our research on a unified framework that addresses this critical challenge in two science domains: computational fluid dynamics and molecular dynamics. We offer a systematic approach to detect the significant features in both domains, characterize and track them, and formulate hypotheses with regard to their complex evolution. Our framework includes two paradigms for feature mining, and the choice of one over the other, for a given application, can be determined based on local or global inn uence of relevant features in the data.
   Bibtex

   @INBOOK{, chapter = {Feature Mining Paradigms for Scientific Data}, pages = {13}, title = {Proceedings of the 2003 SIAM International Conference on Data Mining}, publisher = {SIAM}, year = {2003}, editor = {D. Barbara}, author = {Ming Jiang and Tat-Sang Choy and Sameep Mehta and Matt Coatney and Steve Barr and Kaden Hazzard and David Richie and Srinivasan Parthasarathy and Raghu Machiraju and David Thompson and John Wilkins and Boyd Gatlin} }
2. Large-scale molecular dynamics simulations of interstitial defect diffusion in silicon
   David A. Richie, Jeongnim Kim, Richard Hennig, Kaden R.A. Hazzard, Steve Barr, and John W. Wilkins
   Materials Research Symposium Proceedings, vol. 731, 2002 p. W9. 10-5. (pdf)
   
   Summary

   The simulation of defect dynamics and evolution is a technologically relevant challenge for computational materials science. The diffusion of small defects in silicon unfolds as a sequence of structural transitions. The relative infrequency of transition events requires simulation over extremely long time scales. We simulate the diffusion of small interstitial clusters ($I_1, I_2, I_3$) for a range of temperatures using large-scale molecular dynamics (MD) simulations with a realistic tight-binding potential. A total of 0.25 $\mu$ sec of simulation time is accumulated for the study. A novel real-time multiresolution analysis (RTMRA) technique extracts stable structures directly from the dynamics without structural relaxation. The discovered structures are relaxed to confirm their stability.
   Bibtex

   @ARTICLE{ richie:MD-RTMRA-mrs-proc, author = {David A. Richie and Jeongnim Kim and Richard Hennig and Kaden Hazzard and Steve Barr and John W. Wilkins}, title = {Large-Scale Molecular Dynamics Simulations Of Interstitial Defect Diffusion In Silicon}, journal = {MRS Proceedings}, year = {2002}, volume = {730}, pages = {W9.10} }

Book

1. Quantum phase transitions in cold atoms and low temperature solids
   [[ selected for the ``Springer Theses" book series, a modified version of my thesis ]]
   Kaden R.A. Hazzard
   book page (read online)
   
   Summary

   This thesis describes how to create and probe novel phases of matter and exotic (non-quasiparticle) behavior in cold atomic gases. It focuses on situations whose physics is relevant to condensed matter systems, and where open questions about these latter systems can be addressed. It also attempts to better understand several experimental anomalies in condensed matter systems. See pdf abstract for more details.
   Bibtex

   @BOOK{hazzard:cold-atoms-low-T-book, title = {Quantum phase transitions in cold atoms and low temperature solids}, publisher = {Springer}, year = {2010 (to appear)}, author = {Kaden R. A. Hazzard}, owner = {Kaden}, timestamp = {2010.09.28} }

Contact Kaden