We investigate two-component attractive Fermi gases with imbalanced spin populations in trapped one dimensional configurations. The ground state properties are determined within local density approximation, starting from the exact Bethe-ansatz equations for homogeneous case. predict that atoms distributed according to a two-shell structure: partially polarized phase center of trap and either fully paired or wings. core is expected be superfluid FFLO type. size cloud as well critical...

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

We explore theoretically the dynamical properties of a first-order dissipative phase transition in coherently driven Bose-Hubbard systems, describing, e.g., lattices coupled nonlinear optical cavities. Via stochastic trajectory calculations based on truncated Wigner approximation, we investigate behavior as function system size for one-dimensional (1D) and 2D square regime where mean-field theory predicts bistability. show that critical slowing down emerges increasing number sites lattices,...

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

We present analytical solutions for the mean-field master equation of driven-dissipative Bose-Hubbard model cavity photons, in limit both weak pumping and dissipation. Instead pure Mott-insulator states, we find statistical mixtures with same second-order coherence ${g}^{(2)}(0)$ as a Fock state $n$ but mean photon number $n/2.$ These mixed states occur when pump photons have energy interacting inside nonlinear survive up to critical tunneling coupling strength, above which crossover...

We study the sudden expansion of spin-imbalanced ultracold lattice fermions with attractive interactions in one dimension after turning off longitudinal confining potential. show that momentum distribution functions majority and minority quickly approach stationary values due to a quantum distillation mechanism results spatial separation pairs fermions. As consequence, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations are lost during expansion. Furthermore, we argue shape can be...

Recent experiments on non-interacting ultra-cold atoms in correlated disorder have yielded conflicting results regarding the so-called mobility edge, i.e. energy threshold separating Anderson localized from diffusive states. At same time, there are theoretical indications that experimental data overestimate position of this critical energy, sometimes by a large amount. The non-trivial effect anisotropy spatial correlations speckle potentials been put forward as possible cause for such...

The problem of modeling large driven dissipative quantum systems is tackled with a phase space method, opening the way to progress on myriad experimental platforms described by Bose Hubbard model, including highly non-uniform tens thousands sites.

We calculate the density profiles of a trapped spin-imbalanced Fermi gas with attractive interactions in one-dimensional optical lattice, using both local-density approximation (LDA) and density-matrix renormalization-group (DMRG) simulations. Based on exact equation state obtained by Bethe ansatz, LDA predicts that phase separates into shells partially polarized core fully paired wings, latter occurring below critical spin polarization. This behavior is also seen numerically DMRG...

We investigate one dimensional attractive Fermi gases in spin-dependent optical lattices. show that three-body bound states---``trimers''---exist as soon the two tunneling rates are different. calculate binding energy and effective mass of a single trimer. then numerically for finite commensurate densities ${n}_{\ensuremath{\uparrow}}={n}_{\ensuremath{\downarrow}}/2$ an gap appears, implying gas is one-component Luttinger liquid trimers with suppressed superfluid correlations. The boundaries...

Characterizing the delocalization transition in closed quantum systems with a many-body localized phase is key open question field of nonequilibrium physics. We exploit fact that localization particles as realized Anderson and standard (MBL) implies Fock-space single-particle basis sets characterized by real-space index. Using recently introduced quantitative measure for computed from density distributions, occupation distance, we systematically study its scaling behavior across transitions...

We consider two-component one-dimensional quantum gases with a density imbalance. While generically such fluids are Luttinger liquids, we show that if the ratio of densities is rational number, $p/q$, and mass asymmetry between components sufficiently strong, one two eigenmodes acquires gap. The gapped phase corresponds to (algebraic) ordering ($p+q$)-particle composites. In particular, for attractive mixtures, this implies superconducting correlations destroyed. illustrate our predictions...

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

We investigate numerically the problem of few (one or two) noninteracting spin-$1/2$ fermions in a shallow harmonic trap coupled via contact repulsive interactions to uniform one-dimensional bath lattice bosons, described by Bose-Hubbard model. Through extensive density-matrix renormalization group calculations, we extract binding energy and effective mass quasiparticles, including dressed impurities (polarons) their two-body bound states (bipolarons), emerging from nonlocal Casimir...

We study the molecular behavior of two atoms interacting near a Feshbach resonance in presence 1D periodic potential. The critical value scattering length needed to produce molecule and binding energy at are calculated as function intensity Because non-separability center mass relative motion, depends on quasimomentum molecule. This has dramatic consequences tunneling properties, which become strongly dependent length.

We investigate the problem of two atoms interacting via a short range $s$-wave potential in presence deep optical lattice arbitrary dimension $D$. Using tight-binding approach, we derive analytical results for properties bound state and scattering amplitude. show that tunneling through barriers induces dimensional crossover from confined regime at high energy to an anisotropic three-dimensional low energy. The critical value length needed form two-body shows logaritmic dependence on rate...

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

We investigate the metal-insulator transition occurring in two-dimensional (2D) systems of noninteracting atoms presence artificial spin-orbit interactions and a spatially correlated disorder generated by laser speckles. Based on high order discretization scheme, we calculate precise position mobility edge verify that belongs to symplectic universality class. show depends strongly mixing angle between Rashba Dresselhaus couplings. For equal couplings non-power-law divergence is found,...

We investigate the ground state properties of a disordered superfluid Fermi gas across BCS-BEC (Bose-Einstein condensate) crossover. show that, for weak disorder, both depletion condensate fraction pairs and normal fluid density exhibit nonmonotonic behavior as function interaction parameter $1/{k}_{F}a$, reaching their minimum value near unitarity. find moving away from weak-coupling BCS regime, Anderson's theorem ceases to apply order is more affected by random potential.

Using the time-dependent density matrix renormalization-group method and exact diagonalization, we study nonequilibrium dynamics of one-dimensional Fermi-Hubbard model following a quantum quench or ramp on-site interaction strength. We are particularly interested in evolution Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations, which, at finite spin polarizations for attractive interactions, dominant two-body correlations ground state. For quenches from noninteracting to regime, investigate...

We develop the hydrodynamic theory of Fermi superfluids in presence a periodic potential. The relevant parameters governing propagation sound (compressibility and effective mass) are calculated weakly interacting BCS limit. conditions stability superfluid motion with respect to creation elementary excitations discussed. also evaluate frequency center-of-mass oscillation when gas is additionally confined by harmonic trap.

By solving the Bogoliubov--de Gennes equations at zero temperature, we study effects of a one-dimensional optical lattice on behavior superfluid Fermi gas unitarity. We show that, due to lattice, low densities becomes highly compressible and effective mass is large, with consequent significant reduction sound velocity. discuss role played by in formation molecules emergence two-dimensional equation state. Predictions for density profiles frequency collective oscillations presence harmonic...

Interacting Fermi gases with equal populations but unequal masses are investigated at zero temperature using local density approximation and the hydrodynamic theory of superfluids in presence harmonic trapping. We derive conditions energetic stability superfluid configuration respect to phase separation frequencies collective oscillations terms mass ratio trapping two components. discuss behavior gas after potential a single component is switched off show that, near Feshbach resonance,...

We propose an efficient numerical method to compute configuration averages of observables in disordered open quantum systems whose dynamics can be unraveled via stochastic trajectories. prove that the optimal sampling trajectories and disorder configurations is simply achieved by considering one random for each individual trajectory. As a first application, we exploit present study role on physics driven-dissipative Bose-Hubbard model two different regimes: (i) strong interactions, explore...