Finite systems of bosons and/or fermions described by the Hubbard model can be realized using ultracold atoms confined in optical lattices. The ground states of these systems often exhibit a coexistence of compressible superfluid and incompressible Mott insulating regimes. We analyze such systems by studying the out-of-equilibrium dynamics following a weak sudden quench of the trapping potential. In particular, we show how the temporal variance of the site occupations reveals the location of spatial boundaries between compressible and incompressible regions. The feasibility of this approach is demonstrated for several models using numerical simulations. We first consider integrable systems, hard-core bosons (spinless fermions) confined by a harmonic potential, where space separated Mott and superfluid phases coexist. Then, we analyze a nonintegrable system, a J-V-V' model with coexisting charge density wave and superfluid phases. We find that the temporal variance of the site occupations is a more effective measure than other standard indicators of phase boundaries such as a local compressibility. Based on these examples, we argue that analyzing temporal fluctuations is a valuable experimental tool for exploring phase boundaries in trapped atom systems.

We study the equilibration dynamics of closed finite quantum systems and address the question of the time needed for the system to equilibrate. In particular, we focus on the scaling of the equilibration time T-eq with the system size L. For clean systems, we give general arguments predicting T-eq = O(L-0) for clustering initial states, while for small quenches around a critical point we find T-eq = O(L-zeta) where zeta is the dynamical critical exponent. We then analyze noisy systems where exponentially large time scales are known to exist. Specifically, we consider the tight-binding model with diagonal impurities and give numerical evidence that in this case T-eq similar to Be-CL psi where B, C, psi are observable-dependent constants. Finally, we consider another noisy system whose evolution dynamics is randomly sampled from a circular unitary ensemble. Here, we are able to prove analytically that T-eq = O(1), thus showing that noise alone is not sufficient for slow equilibration dynamics. DOI: 10.1103/PhysRevA.87.032108

Superconducting qubits coupled to electric or nanomechanical resonators display effects previously studied in quantum electrodynamics (QED) as well as extensions thereof. Here, we consider a driven qubit coupled to a low-frequency oscillator and study the influence of dissipation. When the qubit is driven to perform Rabi oscillations, with Rabi frequency in resonance with the oscillator, the latter can be driven far from equilibrium. Blue detuned driving leads to a population inversion in the qubit and lasing behavior of the oscillator ('single-atom laser'). For red detuning, the qubit cools the oscillator. This behavior persists at the symmetry point where the qubit–oscillator coupling is quadratic and decoherence effects are minimized. Here, the system realizes a 'single-atom-two-photon laser'.