Motivated by recent experimental observations [Parker, Hua, and Chin, Nat. Phys. 9, 769 (2013)1745-247310.1038/nphys2789], we analyze the stability of a Bose-Einstein condensate (BEC) in a one-dimensional lattice subjected to periodic shaking. In such a system there is no thermodynamic ground state, but there may be a long-lived steady state, described as an eigenstate of a "Floquet Hamiltonian." We calculate how scattering processes lead to a decay of the Floquet state.

We describe an experimental setup for imaging topologically protected Floquet edge states using ultracold bosons in an optical lattice. Our setup involves a deep two-dimensional optical lattice with a time-dependent superlattice that modulates the hopping between neighboring sites. The finite waist of the superlattice beam yields regions with different topological numbers. One can observe chiral edge states by imaging the real-space density of a bosonic packet launched from the boundary between two topologically distinct regions. © 2014 American Physical Society.

We calculate the ground state of a Bose gas trapped on a two-leg ladder where Raman-induced hopping mimics the effect of a large magnetic field. In the mean-field limit, where there are large numbers of particles per site, this maps onto a uniformly frustrated two-leg ladder classical spin model. The net particle current always vanishes in the ground state, but generically there is a finite "chiral current," corresponding to equal and opposite flow on the two legs. We vary the strength of the hopping across the rungs of the ladder and the interaction between the bosons.

We show how to exploit the rich hyperfine structure of fermionic alkali-metal atoms to produce a quasi-one-dimensional (quasi-1D) topological superfluid while avoiding excessive heating from off-resonant scattering. We model interacting fermions where four hyperfine states are coupled by a variety of optical and microwave fields. We calculate the local density of states in a trap, finding regimes with zero-energy topological edge modes. Heating rates in this system are significantly suppressed compared to simple Raman-induced spin-orbit coupling approaches.

We describe how microwave spectroscopy of cold fermions in quasi-1D traps can be used to detect, manipulate, and entangle exotic nonlocal qubits associated with "Majorana" edge modes. We present different approaches to generate the p-wave superfluidity which is responsible for these topological zero-energy edge modes. We find that the edge modes have clear signatures in the microwave spectrum and that the line shape distinguishes between the degenerate states of a qubit encoded in these edge modes. Moreover, the microwaves rotate the system in its degenerate ground-state manifold.

We use the time-dependent Gross-Pitaevskii equation to study the motion of a vortex ring produced by phase imprinting on an elongated cloud of cold atoms. Our approach models the experiments of Yefsah on 6Li in the Bose-Einstein- condensate regime where the fermions are tightly bound into bosonic dimers. We find ring oscillation periods which are much larger than the period of the axial harmonic trap. Our results lend further strength to Bulgac 's arguments (arXiv:1306.4266) that the "heavy solitons" seen in those experiments are actually vortex rings.

We use variational methods to study a spin impurity in a one-dimensional Bose lattice gas. Both in the strongly interacting superfluid regime and in the Mott regime we find that the impurity binds with a hole, forming a polaron. Our calculations for the dispersion of the polaron are consistent with recent experiments by Fukuhara and give a better understanding of their numerical simulations. We find that for sufficiently weak interactions there are ranges of momentum for which the polaron is unstable.

We calculate the radio frequency (RF) spectrum of fermionic atoms near a narrow Feshbach resonance, explaining observations made in ultracold samples of 6Li. We use a two channel resonance model to show that the RF spectrum contains two peaks. In the wide-resonance limit, nearly all spectral weight lies in one of these peaks, and typically the second peak is very broad. We find strong temperature dependence, which can be traced to the energy dependence of the two-particle scattering.

We explore the time evolution of correlations in a homogeneous gas of lattice bosons with filling factor n0, following a sudden reduction in the lattice depth to a regime where the interactions are weak. In the limit of vanishing interactions, we find a simple closed-form expression for the static structure factor. The corresponding real-space density-density correlation function shows multiple spatial oscillations which disperse linearly in time. By perturbatively including the effect of interactions, we study the evolution of boson quasimomentum distribution following the quench.