We calculate the effect of interactions on the expansion of ultracold atoms from a single site of an optical lattice. We use these results to predict how interactions influence the interference pattern observed in a time-of-flight experiment. We find that for typical interaction strengths their influence is negligible, yet that they reduce visibility near a scattering resonance. © 2010 The American Physical Society.

We study how different many-body states appear in a quantum-gas microscope, such as the one developed at Harvard, where the site-resolved parity of the atom number is imaged. We calculate the spatial correlations of the microscope images, corresponding to the correlation function of the parity of the number of atoms at each site. We produce analytic results for a number of well-known models: noninteracting bosons, the large-U Bose-Hubbard model, and noninteracting fermions.

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. © 2010 The American Physical Society.

We model the dynamics of two species of bosonic atoms trapped in an optical lattice within the Mott regime by mapping the system onto a spin model. A field gradient breaks the cloud into two domains. We study how the domain wall evolves under adiabatic and diabatic changes of this gradient. We determine the time scales for adiabaticity and study how temperature evolves for slow ramps. We show that after large, sudden changes of the field gradient, the system does not equilibrate on typical experimental time scales.

We perform variational Monte Carlo calculations to show that bosons in a rotating optical lattice will form analogs of fractional quantum Hall states when the tunneling is sufficiently weak compared to the interactions, and the deviation of density from an integer is commensurate with the effective magnetic field. We compare the energies of superfluid and correlated states to one another and to the energies found in full configuration-interaction calculations on small systems.

We present a theory of spin waves in a noncondensed gas of spin-1 bosons and provide both analytic calculations of the linear theory and full numerical simulations of the nonlinear response. We highlight the role of spin-dependent contact interactions in the dynamics of a thermal gas. Although these interactions are small compared to the thermal energy, they set the scale for low-energy, long-wavelength spin waves. In particular, we find that the polar state of Rb87 is unstable to collisional mixing of magnetic sublevels even in the normal state.

We study the three-fermion problem within a 1D model of a Feshbach resonance in order to gain insight into how the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state at small negative scattering lengths evolves into a Bose-Fermi mixture at small positive scattering lengths. The FFLO state possesses an oscillating superfluid correlation function, while in a Bose-Fermi mixture correlations are monotonic. We find that this behavior is already present at the three-body level.

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.

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 and 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.

Antiferromagnetism of ultracold fermions in an optical lattice can be detected by Bragg diffraction of light, in analogy to the diffraction of neutrons from solid-state materials. A finite sublattice magnetization will lead to a Bragg peak from the (121212) crystal plane with an intensity depending on details of the atomic states, the frequency and polarization of the probe beam, the direction and magnitude of the sublattice magnetization, and the finite optical density of the sample.