Giuliano Orso

Steady-state phases and tunneling-induced instabilities in the driven dissipative Bose-Hubbard model.

We determine the steady-state phases of a driven-dissipative Bose-Hubbard model, describing, e.g., an array of coherently pumped nonlinear cavities with a finite photon lifetime. Within a mean-field master equation approach using exact quantum solutions for the one-site problem, we show that the system exhibits a tunneling-induced transition between monostable and bistable phases. We characterize the corresponding quantum correlations, highlighting the essential differences with respect to the equilibrium case. We also find collective excitations with a flat energy-momentum dispersion over the entire Brillouin zone that trigger modulational instabilities at specific wave vectors.

Anderson localization of pairs in bichromatic optical lattices

We investigate the formation of bound states made of two interacting atoms moving in a one dimensional (1D) quasiperiodic optical lattice. We derive the quantum phase diagram for Anderson localization of both attractively and repulsively bound pairs. We calculate the pair binding energy and show analytically that its behavior as a function of the interaction strength depends crucially on the nature-extended, multifractal, localized-of the single-particle atomic states. Experimental implications of our results are discussed.

Mobility edge for cold atoms in laser speckle potentials.

Using the transfer-matrix method, we numerically compute the precise position of the mobility edge of atoms exposed to a laser speckle potential and study its dependence versus the disorder strength and correlation function. Our results deviate significantly from previous theoretical estimates using an approximate, self-consistent approach of localization. In particular, we find that the position of the mobility edge in blue-detuned speckles is much lower than in the red-detuned counterpart, pointing out the crucial role played by the asymmetric on-site distribution of speckle patterns.

Bose-Hubbard Model: Relation Between Driven-Dissipative Steady-States and Equilibrium Quantum Phases

We present analytical solutions for the mean-field master equation of the driven-dissipative Bose-Hubbard model for cavity photons, in the limit of both weak pumping and weak dissipation. Instead of pure Mott insulator states, we find statistical mixtures with the same second-order coherence as a Fock state with n photons, but a mean photon number of n/2. These mixed states occur when n pump photons have the same energy as n interacting photons inside the nonlinear cavity and survive up to a critical tunneling coupling strength, above which a crossover to classical coherent state takes place. We also explain the origin of both antibunching and superbunching predicted by P-representation mean-field theory at higher pumping and dissipation. In particular, we show that the strongly correlated region of the associated phase diagram cannot be described within the semiclassical Gross-Pitaevski approach.

Long-time behavior of the momentum distribution during the sudden expansion of a spin-imbalanced Fermi gas in one dimension.

We study the sudden expansion of spin-imbalanced ultracold lattice fermions with attractive interactions in one dimension after turning off the longitudinal confining potential. We show that the momentum distribution functions of majority and minority fermions quickly approach stationary values due to a quantum distillation mechanism that results in a spatial separation of pairs and majority fermions. As a consequence, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations are lost during the expansion. Furthermore, we argue that the shape of the stationary momentum distribution functions can be understood by relating them to the integrals of motion in this integrable quantum system. We discuss our results in the context of proposals to observe FFLO correlations, related to recent experiments by Liao et al., Nature (London) 467, 567 (2010).

Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains.

We simulate numerically the dynamics of strongly correlated bosons in a two-leg ladder subject to a time-dependent energy bias between the two chains. When all atoms are initially in the leg with higher energy, we find a drastic reduction of the interchain particle transfer for slow linear sweeps, in quantitative agreement with recent experiments. This effect is preceded by a rapid broadening of the quasimomentum distribution of atoms, signaling the presence of a bath of low-energy excitations in the chains. We further investigate the scenario of quantum quenches to fixed values of the energy bias. We find that for a large enough density the momentum distribution relaxes to that of an equilibrium thermal state with the same energy.

Anderson Localization of Ultracold Atoms: Where is the Mobility Edge?

Recent experiments in noninteracting ultracold atoms in three-dimensional speckle potentials have yielded conflicting results regarding the so-called mobility edge, i.e., the energy threshold separating Anderson localized from diffusive states. At the same time, there are theoretical indications that most experimental data overestimate this critical energy, sometimes by a large amount. Using extensive numerical simulations, we show that the effect of anisotropy in the spatial correlations of realistic disorder configurations alone is not sufficient to explain the experimental data. In particular, we find that the mobility edge obeys a universal scaling behavior, independently of the speckle geometry.

Fermionic trimers in spin-dependent optical lattices

We investigate the formation of three-body bound states (trimers) in two-component Fermi gases confined in a one-dimensional optical lattice with spin-dependent tunneling rates. The binding energy and the effective mass of the trimer are obtained from the solution of the Mattis integral equation generalized to the case of unequal Bloch masses. We show that this equation admits multiple solutions corresponding to excited bound states, which are only stable for large mass asymmetry

Phase diagram of the three-dimensional Anderson model for short-range speckle potentials

A discrepancy between existing theories and essentially exact numerical results on the asymmetry of the mobility edge for Anderson localization is now resolved, where an improved single-particle Greens function \char22{} a crucial component that could be used in existing theories for other relevant studies \char22{} is found to bridge the gap.

Low-dimensional physics of ultracold gases with bound states and the sine-Gordon model

One-dimensional systems of interacting atoms are an ideal laboratory to study the Kosterlitz-Thouless phase transition. In the renormalization group picture there is essentially a two-parameter phase diagram to explore. We first present how detailed experiments have shown direct evidence for the theoretical treatment of this transition. Then generalization to the case of two-component systems with bound state formation is discussed. Trimer formation in the asymmetric attractive Hubbard model involve in a crucial way this kind of physics.