We calculate how correlations in a Bose lattice gas grow during a finite-speed ramp from the Mott to the superfluid regime. We use an interacting doublon-holon model, applying a mean-field approach for implementing hard-core constraints between these degrees of freedom. Our solutions are valid in any dimension and agree with experimental results and with density matrix renormalization group calculations in one dimension. We find that the final energy density of the system drops quickly with increased ramp time for ramps shorter than one hopping time, JÏ„ramp1.

We explore the effect of transverse confinement on the stability of a Bose-Einstein condensate loaded in a shaken one-dimensional or two-dimensional square lattice. We calculate the decay rate from two-particle collisions. We predict that if the transverse confinement exceeds a critical value, then, for appropriate shaking frequencies, the condensate is stable against scattering into transverse directions. We explore the confinement dependence of the loss rate, explaining the rich structure in terms of resonances. © 2015 American Physical Society.

We model atomic motion in a sliding superlattice potential to explore "topological charge pumping" and to find optimal parameters for experimental observation of this phenomenon. We analytically study the band structure, finding how the Wannier states evolve as two sinusoidal lattices are moved relative to one another, and relate this evolution to the center-of-mass motion of an atomic cloud. We pay particular attention to counterintuitive or anomalous regimes, such as when the atomic motion is opposite to that of the lattice.

We compute the spectral density in the normal phase of an interacting homogenous Fermi gas using a T-matrix approximation. We fit the quasiparticle peaks of the spectral density to BCS-like dispersion relations and extract estimates of a "pseudogap" energy scale and an effective Fermi wave vector as a function of interaction strength. We find that the effective Fermi wave vector of the quasiparticles vanishes when the inverse scattering length exceeds some positive threshold.

We study the collisionless spin dynamics of a harmonically trapped Fermi gas in a magnetic field gradient. In the absence of interactions, the system evolution is periodic: the magnetization develops twists, which evolve into a longitudinal polarization. Recurrences follow. For weak interaction, the exchange interactions lead to beats in these oscillations. We present an array of analytic and numerical techniques for studying this physics. © 2015 American Physical Society.

By returning to the underlying discrete time formalism, we relate spurious results in coherent state semiclassical path integral calculations, i.e. those involving quadratic fluctuations about classical paths, to the high frequency structure of their propagators. We show how to modify the standard expressions for thermodynamic quantities to yield correct results. These expressions are relevant to a broad range of physical problems, from the thermodynamics of Bose lattice gases to the dynamics of spin systems. © 2015, EDP Sciences and Springer.

Motivated by recent experiments, we analyze the stability of a three-dimensional Bose-Einstein condensate loaded in a periodically driven one-dimensional optical lattice. Such periodically driven systems do not have a thermodynamic ground state but may have a long-lived steady state which is an eigenstate of a "Floquet Hamiltonian." We explore collisional instabilities of the Floquet ground state which transfer energy into the transverse modes.

We model the dynamics of condensation in a bimodal trap, consisting of a large reservoir region, and a tight "dimple" whose depth can be controlled. Experimental investigations have found that such dimple traps provide an efficient means of achieving condensation. In our kinetic equations, we include two- and three-body processes. The two-body processes populate the dimple, and lead to loss when one of the colliding atoms is ejected from the trap. The three-body processes produce heating and loss.

We explore the effects of continuous number density measurement on atoms in an optical lattice. By integrating a master equation for quantum observables, we calculate how single-particle correlations decay. We consider weakly and strongly interacting bosons and noninteracting fermions. Even in the Mott regime, such measurements destroy correlations and increase the average energy, as long as some hopping is allowed. We explore the role of spatial resolution and find that the heating rate is proportional to the amount of information gained from such measurements.