My recent research evolved in several directions, for example rapidly rotating gases and fractional quantum hall physics, novel consequences of strong interactions in lattices, and reduced dimensional quantum gases.

*The rf spectrum as a function of chemical potential and hopping rate with
opacity indicating spectral weight; 20% different initial and final state interactions.
*

Cold atoms offer many appealing features for studying many-body systems: (i) one knows exactly the Hamiltonian, which often is a canonical solid state model, such as a Hubbard model; (ii) they are quantum coherent on experimentally relevant timescales --- they couple to no bath; and (iii) their behavior is readily tunable: for example, one may greatly vary the interaction strength, band structure, and internal spin structure. However, our probes at the moment are rather blunt. The most common is absorption imaging, which provides real space column-integrated densities.

Top: cartoon of superfluid near the Mott instability, for average site fillings slightly greater than 3. Near the Mott state, the superfluid state looks like a Mott insulator with a few delocalized particles or holes dispersed on it. Bottom: After absorbing an rf photon to change an atom's internal state, there are two possible final states, each with different energies, leading to a bimodal rf spectra.

In contrast, spectroscopies cleanly distinguish these scenarios by probing their excitations:
each has a characteristic number of excitations, gapless or gapped
dispersion, and spectral weight distribution.
Erich and I have concentrated on rf-microwave spectroscopy of bosons in an
optical lattice, in which absorbed photons change only the internal state of
atoms. Hazzard and Mueller, PRA
**76 **063612 (2007) calculated the
trap-averaged rf spectra, using a sum rule approach assuming that
the local spectrum was a single delta function. As a follow up, we have been
investigating the full local structure of the rf spectra.
In work being prepared for publication, we find that the superfluid near the
Mott instability displays a multi-peaked spectrum, one peak with "Mott"
and one with "delocalized" behavior; the dual nature of these correlations
are illustrated to the left. The
characteristic spectral densities are to the right and at the top right of the
page.

*Left: spectral
density as a function of frequency and distance to trap center (white).
Right: trap averaged spectral density (solid) versus frequency (on vertical
axis). Red curves are predictions of the sum rule approach. *

I believe rf spectroscopy will continue to play an important role in cold atoms. For vanishing final state interactions, rf spectra are quasi-hole spectra; for equal final and initial state interactions, it is an analog of Bragg scattering/spectroscopy and transport measurements. Each are standard, powerful solid state probes. By varying the final state interaction, we may mimic these techniques and additionally "interpolate" between these two limits. Consequently, although the present theory and experiment has largely restricted to zero momentum excitations, extending this work to finite momenta would be valuable. I hope that our work enables an even better understanding of the bosonic Mott insulator and helps pave the way for further application of spectroscopy to cold atomic many body systems.