Nonequilibrium Dynamics and Weakly Broken Integrability.

Motivated by dynamical experiments on cold atomic gases, we develop a quantum kinetic approach to weakly perturbed integrable models out of equilibrium. Using the exact matrix elements of the underlying integrable model, we establish an analytical approach to real-time dynamics. The method addresses a broad range of timescales, from the intermediate regime of prethermalization to late-time thermalization.

Quantum Quenches in Chern Insulators.

We explore the nonequilibrium response of Chern insulators. Focusing on the Haldane model, we study the dynamics induced by quantum quenches between topological and nontopological phases. A notable feature is that the Chern number, calculated for an infinite system, is unchanged under the dynamics following such a quench.

Fermionic superradiance in a transversely pumped optical cavity.

Following the experimental realization of Dicke superradiance in Bose gases coupled to cavity light fields, we investigate the behavior of ultracold fermions in a transversely pumped cavity. We focus on the equilibrium phase diagram of spinless fermions coupled to a single cavity mode and establish a zero temperature transition to a superradiant state. In contrast to the bosonic case, Pauli blocking leads to lattice commensuration effects that influence self-organization in the cavity light field.

Holographic superfluids and the dynamics of symmetry breaking.

We explore the far-from-equilibrium response of a holographic superfluid using the AdS/CFT correspondence. We establish the dynamical phase diagram corresponding to quantum quenches of the order parameter source field. We find three distinct regimes of behavior that are related to the spectrum of black hole quasinormal modes.

Ising deconfinement transition between Feshbach-resonant superfluids.

We investigate the phase diagram of bosons interacting via Feshbach-resonant pairing interactions in a one-dimensional lattice. Using large scale density matrix renormalization group and field theory techniques we explore the atomic and molecular correlations in this low-dimensional setting. We provide compelling evidence for an Ising deconfinement transition occurring between distinct superfluids and extract the Ising order parameter and correlation length of this unusual superfluid transition.

Collective dynamics of Bose-Einstein condensates in optical cavities.

Experiments on Bose-Einstein condensates in optical cavities have observed a coherent state of the matter-light system-superradiance. The nature of these experiments demands consideration of collective dynamics. Including cavity leakage and the backreaction of the cavity field on the condensate, we find a rich phase diagram including multiphase coexistence regions, and persistent optomechanical oscillations.

Feshbach resonance in optical lattices and the quantum Ising model.

Motivated by experiments on heteronuclear Feshbach resonances in Bose mixtures, we investigate s-wave pairing of two species of bosons in an optical lattice. The zero temperature phase diagram supports a rich array of superfluid and Mott phases and a network of quantum critical points. This topology reveals an underlying structure that is succinctly captured by a two-component Landau theory.

Polaritons and pairing phenomena in Bose-Hubbard mixtures.

Motivated by recent experiments on cold atomic gases in ultrahigh finesse optical cavities, we consider the two-band Bose-Hubbard model coupled to quantum light. Photoexcitation promotes carriers between the bands, and we study the interplay between Mott insulating behavior and superfluidity. The model displays a U(1)xU(1) symmetry which supports the coexistence of Mott insulating and superfluid phases and yields a rich phase diagram with multicritical points.

Magnetothermoelectric response at a superfluid-Mott-insulator transition.

We investigate the finite temperature magnetothermoelectric response in the vicinity of a superfluid-Mott-insulator quantum phase transition. We focus on the particle-hole symmetric transitions of the Bose-Hubbard model, and combine Lorentz invariance arguments with quantum Boltzmann calculations. By means of an epsilon expansion, we find that a nonvanishing thermoelectric tensor and a finite thermal transport coefficient are supported in this quantum critical regime.