We analyze the single-particle quantum mechanics of an atom whose dispersion is modified by spin-orbit coupling to Raman lasers. Such a setup can create a double-well-shaped dispersion, which leads to unusual single-particle physics. We show how this dispersion influences the symmetry of the ground-state wave function in different physical-space potentials, including a square well, a harmonic well, and a double well. © 2012 American Physical Society.

We calculate the vortex structures of an elongated two-component Bose-Einstein condensate. We study how these structures depend on the intracomponent and intercomponent interaction strengths. We present analytical and numerical results respectively at weak and strong interactions; finding lattices with different interlocking geometries: triangular, square, rectangular, and double core. © 2011 American Physical Society.

We find the conditions under which the normal state of a spin-1 Bose gas is unstable toward condensation, ferromagnetism, liquid crystalline-like nematicity, and Bardeen-Cooper-Schrieffer-like pairing. When the spin-dependent interactions are much weaker than the density-density interaction there is direct transition from a featureless normal state to a fully ordered Bose-Einstein condensate with either ferromagnetic or nematic order.

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. © 2011 American Physical Society.

We calculate the single-particle spectral density of a normal (nonsuperfluid) two-component gas of fermions in the BCS-BEC crossover within a T-matrix approximation. We review how noncondensed pairs lead to a spectral density reminiscent of the ordered state, and explore how a gaplike feature in the spectrum evolves as one changes the polarization of the gas. As the gas is polarized, we find that this pseudogap becomes more diffuse and moves away from the Fermi level, reflecting the fact that fewer pairs are present but that they still play an important role in the excitations.

We show how interpenetrating optical lattices containing Bose-Fermi mixtures can be constructed to emulate the thermodynamics of quantum electrodynamics (QED). We present models of neutral atoms on lattices in 1+1, 2+1, and 3+1 dimensions whose low-energy effective action reduces to that of photons coupled to Dirac fermions of the corresponding dimensionality. We give special attention to (2+1)-dimensional quantum electrodynamics (QED3) and discuss how two of its most interesting features, chiral symmetry breaking and Chern-Simons physics, could be observed experimentally.

We study the time scales for adiabaticity of trapped cold bosons subject to a time-varying lattice potential using a dynamic Gutzwiller mean-field theory. We explain apparently contradictory experimental observations by demonstrating a clear separation of time scales for local dynamics (∼ms) and global mass redistribution (∼1s). We provide a simple explanation for the short and fast time scales, finding that while density or energy transport is dominated by low energy phonons, particle-hole excitations set the adiabaticity time for fast ramps.

We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model.

Superconductivity and magnetism generally do not coexist. Changing the relative number of up and down spin electrons disrupts the basic mechanism of superconductivity, where atoms of opposite momentum and spin form Cooper pairs. Nearly forty years ago Fulde and Ferrell and Larkin and Ovchinnikov (FFLO) proposed an exotic pairing mechanism in which magnetism is accommodated by the formation of pairs with finite momentum. Despite intense theoretical and experimental efforts, however, polarized superconductivity remains largely elusive.

We study entropy generation in a one-dimensional (1D) model of bosons in an optical lattice experiencing two-particle losses. Such heating is a major impediment to observing exotic low temperature states, and " simulating" condensed matter systems. Developing intuition through numerical simulations, we present a simple empirical model for the entropy produced in this 1D setting. We also explore the time evolution of one- and two-particle correlation functions, showing that they are robust against two-particle loss.