Motivated by recent experiments, we explore the kinetics of Bose-Einstein condensation in the upper band of a double-well optical lattice. These experiments engineer a nonequilibrium situation in which the highest energy state in the band is macroscopically occupied. The system subsequently relaxes and the condensate moves to the lowest energy state.

We construct and characterize tight-binding Hamiltonians which contain a completely flat topological band made of continuum lowest Landau-level wave functions sampled on a lattice. We find an infinite family of such Hamiltonians, with simple analytic descriptions. These provide a valuable tool for constructing exactly solvable models. We also implement a numerical algorithm for finding the most local Hamiltonian with a flat Landau level. We find intriguing structures in the spatial dependence of the matrix elements for this optimized model.

Motivated by recent experiments, we model the dynamics of bright solitons formed by cold gases in quasi-1D traps. A dynamical variational Ansatz captures the far-from-equilibrium excitations of these solitons. Due to a separation of scales, the radial and axial modes decouple, allowing for closed-form approximations for the dynamics. We explore how soliton dynamics influence atom loss and find that the time-averaged loss is largely insensitive to the degree of excitation.

We propose an experimental protocol for using cold atoms to create and probe quantum dimer models, thereby exploring the Pauling-Anderson vision of a macroscopic collection of resonating bonds. This process can allow the study of exotic crystalline phases, fractionalization, topological spin liquids, and the relationship between resonating dimers and superconductivity subjects which have been challenging to address in solid-state experiments.

We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: A quantum computation approach in which errors are prevented and corrected in part by repeatedly measuring redundant degrees of freedom. We show how to construct a set of projective measurements which will map between two arbitrary stabilizer codes. We show that this process preserves all quantum information.

We present and analyze a protocol in which polaritons in a noncoplanar optical cavity form fractional quantum Hall states. We model the formation of these states and present techniques for subsequently creating anyons and measuring their fractional exchange statistics. In this protocol, we use a rapid adiabatic passage scheme to sequentially add polaritons to the system, such that the system is coherently driven from n- to (n+1)-particle Laughlin states. Quasiholes are created by slowly moving local pinning potentials in from outside the cloud.

We analyze an experimentally realizable model of bosons in a zigzag optical lattice, showing that, by rapidly modulating the magnetic field, one can tune interaction parameters and realize an analog of the Haldane phase. We explain how quantum gas microscopy can be used to detect this phase's nonlocal string order and its topological edge states. We model the detection process. We also find that this model can display supersolid correlations, but argue that they only occur at parameter values which would be challenging to realize in an experiment. © 2018 American Physical Society.

A central challenge in modern condensed matter physics is developing the tools for understanding nontrivial yet unordered states of matter. One important idea to emerge in this context is that of a 'pseudogap': the fact that under appropriate circumstances the normal state displays a suppression of the single particle spectral density near the Fermi level, reminiscent of the gaps seen in ordered states of matter. While these concepts arose in a solid state context, they are now being explored in cold gases.

We propose a two-step experimental protocol to directly engineer Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a cold two-component Fermi gas loaded into a quasi-one-dimensional trap. First, one uses phase imprinting to create a train of domain walls in a superfluid with equal number of ↑- and ↓-spins. Second, one applies a radio-frequency sweep to selectively break Cooper pairs near the domain walls and transfer the ↑-spins to a third spin state, which does not interact with the ↑- and ↓-spins.

We characterize the collective modes of a soliton train in a quasi-one-dimensional Fermi superfluid, using a mean-field formalism. In addition to the expected Goldstone and Higgs modes, we find novel long-lived gapped modes associated with oscillations of the soliton cores. The soliton train has an instability that depends strongly on the interaction strength and the spacing of solitons. It can be stabilized by filling each soliton with an unpaired fermion, thus forming a commensurate Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase.