Publications

My work :

Post-2005, the arxiv list is complete.

Preprints

Synthetic dimensions in ultracold molecules: quantum strings and membranes
Bhuvanesh Sundar, Bryce Gadway, and Kaden R. A. Hazzard
arxiv:1708.02112 (pdf)

Summary

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 synthetic inter-site tunnelings with fully controllable magnitudes and phases. When molecules are frozen in a periodic real space array with uniform synthetic tunnelings, the system undergoes a spontaneous dimensional reduction beyond a critical value of the dipole interaction. In this state, the system collapses to a narrow strip in the synthetic direction, resulting in a quantum string (for a 1D chain of molecules) or a membrane (for a 2D array). At large interactions, an emergent strongly interacting condensate lives on the string or membrane. In a 2D array of molecules, we also find evidence of a metastable non-Abelian Ising anyon phase. We show that all these phases can be detected using local measurements of rotational state populations.

Bibtex

@Article{sundar:synthetic_2017, author = {Bhuvanesh Sundar and Bryce Gadway and Kaden R. A. Hazzard}, title = {Synthetic dimensions in ultracold molecules: quantum strings and membranes}, journal = {arxiv:1708.02112} }
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
arxiv:1707.00343 (pdf)

Summary

We compute physical properties across the phase diagram of the $t$-$J_\perp$ chain with long-range dipolar interactions, which describes ultracold polar molecules on optical lattices. Our results obtained by the density matrix renormalization group (DMRG) 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{manmana:correlations, author = {Salvatore R. Manmana and Marcel M{\"o}ller and Riccardo Gezzi and Kaden R. A. Hazzard}, title = {Correlations and enlarged superconducting phase of $t$-$J_\perp$ chains of ultracold molecules on optical lattices}, journal = {arxiv:1707.00343} }
Bosonic molecules in a lattice: unconventional phases from multichannel interactions
Kevin D. Ewart, Michael L. Wall, and Kaden R. A. Hazzard
arxiv:1706.00539 (pdf)

Summary

We show that multichannel interactions dramatically 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. We calculate the phase diagram using complementary methods, including Gutzwiller mean-field and density matrix renormalization group (DMRG) 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{ewart:bosonic_2017, author = {Kevin D. Ewart and Michael L. Wall and Kaden R. A. Hazzard}, title = {Bosonic molecules in a lattice: unconventional phases from multichannel interactions}, journal = {arxiv:1706.00539} }
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
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_2016, author = {Rick Mukherjee and Anthony E. Mirasola and Jacob Hollingsworth and Ian G. White and Kaden R. A. Hazzard}, title = {Geometric representation of spin correlations and applications to ultracold systems}, journal = {arxiv:1612.06459} }
Correlations generated from high-temperature states: nonequilibrium dynamics in the Fermi-Hubbard model
Ian G. White, Randall G. Hulet, and Kaden R. A. Hazzard
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 non-interacting 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, author = {Ian G. White and Randall G. Hulet and Kaden R. A. Hazzard}, title = {Correlations generated from high-temperature states: nonequilibrium dynamics in the Fermi-Hubbard model}, journal = {arxiv:1612.05671} }

Journal publications

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} }
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} }
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} } }
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} }
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} }
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} }
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} }
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} }
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} }
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
}, owner = {Kaden}, timestamp = {2015.06.13} }
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} }
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} }
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} }
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} }
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} }
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}}
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} }
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} }
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} }
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} }
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} }
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} }
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} }
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} }
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} }
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} }
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} }
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} }
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} }
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} }
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} }
Stirring trapped atoms into Fractional Quantum Hall puddles
Kaden R.A. Hazzard, Stefan K. Baur, 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} }
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} }
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} }
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} }
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} }
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

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}, }
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} }
Molecular dynamics as a bridge: fundamentals, methods, and current research
Kaden R.A. Hazzard
Reviews in Undergraduate Research, vol. 1, issue 2, 2003

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} }
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} }
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

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} }

Hazzard group

ultracold atoms and condensed matter theory

My work :

Preprints

Journal publications

Proceedings and other refereed publications with results unavailable elsewhere

Book

Contact Kaden