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Ultracold Fermi atoms confined in optical lattices coupled to quantized modes of an optical cavity are an ideal scenario to engineer quantum simulators in the strongly interacting regime. The system has both short range and cavity induced long range interactions. We propose such a scheme to investigate the coexistence of superfluid pairing, density order and quantum domains having antiferromagnetic or density order in the Hubbard model in a high finesse optical cavity at T = 0. We demonstrate that those phases can be accessed by properly tuning the linear polarizer of an external pump beam via the cavity back-action effect, while modulating the system doping. This allows emulate the typical scenarios of analog strongly correlated electronic systems.Introduction. Coupling ultracold quantum gases to high-finesse optical cavities is a novel scenario to explore many-body phases in the full quantum regime by exploiting the controllability of light-matter interaction [1,2]. Major experimental breakthroughs have been achieved in the quantum limit of both light and matter. For instance, the Dicke phase transition has been observed in a Bose-Einstein condensate coupled to cavity modes [3]. Experimentally, it has been achieved the emergence and control of supersolid phases where the cavity backaction generates light-induced effective long-range interactions which compete with short-range interatomic interactions [4][5][6][7][8].On the theoretical side, recent studies have introduced settings where cavity fields generate gauge-fields [9, 10], artificial spin-orbit coupling [11], self-organized phases [12,13], topological phases [14,15], measurement induced entangled modes [16], induced magnetic and density order using measurement back action [17] and feedback control [18], dimerization [19], spin lattice systems [20] and quantum simulators based on global collective lightmatter interactions [21,22].

Using mean-field theory for the Bardeen-Cooper-Schriefer (BCS) to the Bose-Einstein condensate (BEC) crossover we investigate the ground state thermodynamic properties of an interacting homogeneous Fermi gas. The interatomic interactions modeled through a finite range potential allows us to explore the entire region from weak to strong interacting regimes with no approximations.To exhibit the thermodynamic behavior as a function of the potential parameters in the whole crossover region, we concentrate in studying the Contact variable, the thermodynamic conjugate of the inverse of the s-wave scattering length. Our analysis allows us to validate the mean-field approach across the whole crossover. It also leads to predict a quantum phase transition-like in the case when the potential range becomes large. This finding is a direct consequence of the k-dependent energy gap for finite interaction range potentials.

Quantum states of a two-component Fermi trapped gas are described by introducing an effective trap frequency, determined via variational techniques. Closed expressions for the contribution of a contact interaction potential to the total energy and the pairing interaction are derived. They are valid for both few and large number of particles, given the discrete nature of the formulation, and therefore richer than the continuous expressions, which are perfectly matched. Pairing energies within a shell are explicitly evaluated and its allowed values at a given energy level delimited. We show the importance of the interaction over the trap energy as the number of particles (N ) grows and the temperature decreases. At zero temperature we find a polynomial dependence of the interaction energy on the Fermi energy, whose dominant term at large N corresponds with the mean field approximation result. In addition, the role of the strength of an attractive potential on the total energy is exhibited.

We perform a variational quantum Monte Carlo simulation of an interacting Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based on the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the BCS and BEC regimes as a function of the scattering length. Energies, densities and correlation functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are performed including the verification of the virial relation and the evaluation of the β parameter.PACS numbers: 03.75. Ss, 03.75.Hh, 05.30.Fk The crossover from a low interacting attractive Bardeen-Cooper-Schieffer (BCS) gas to a molecular BoseEinstein condensate (BEC) has been realized experimentally using a mixture of ultracold Fermi atoms in two hyperfine states [1,2,3,4,5]. In dilute Fermi gases, the atomic interactions have a range much smaller than the interparticle separation. Nevertheless, under proper conditions, a magnetic field can be used to tune the attractive potential so that the energy of a pair of scattering atoms is close to that of a molecular bound state (Feshbach resonance). In experiments where the resonance is broad, it can be represented by a single-channel model in which the s-wave scattering length a determines the general features of the ultracold atomic gas. At low enough temperatures, atoms in different hyperfine states pair into bound molecules for positive values of a, forming a molecular BEC that can be adiabatically converted into a degenerate Fermi gas by shifting a to negative values. At resonance (|a| → ∞), the gas acquires universal properties, i. e., they are independent of any feature of the atomic potentials [2,6,7]. This is the so called unitarity limit.The theoretical description of the BEC-BCS crossover is complicated because there is no ad hoc single parameter to control the relevant features in both regimes. A reasonable alternative to infer properties of the system at unitarity has been to consider an homogeneous Fermi gas, and to assume the universality hypothesis according to which the only dominant length is the interparticle separation. Then, the thermodynamic potentials have a universal form specified by only few universal numbers [7]. For instance, the interaction energy is proportional to the Fermi energy via a universal constant β.Quantum Monte Carlo (QMC) techniques support ab initio methods to theoretically test the universality hypothesis. They can be used to approximately solve the many-body Schrödinger equation for a given model of the interaction potential. In previous studies the BEC and BCS regimes have been explored using a fixed-node QMC technique, which is rigorous but also computationally demanding. In particular, the value of β has been predicted considering up to 66 particles [8,9]. Nevertheless, these QMC calcu...

The system under study consists of an interacting ultracold Bose gas confined by a finite n-well potential in one dimension (n = 2, 3 and 4). By numerically solving the time-dependent Schrödinger equation for the effective Hamiltonian that describes the gas confined in each potential, we determine the mean population of particles in each well as a function of time. From this analysis, we obtain a continuous transition from a coherent state to a self-trapped state as a function of the parameter Λ ≈ Ng, which takes into account the number of particles N and the interaction strength g in each system. Three different behaviours as a function of Λ are found: a coherent oscillation regime, a partial-trapped state and a self-trapped state. The partial trapping regime appears to be a novel phase for finite potentials in one dimension. A systematic quantitative study allows us to conclude that the relaxation time observed in the coherent oscillation regime for a two-well potential scales as N1/2. Finally, a comparison with an experimental realization of a Bose–Einstein condensate in a two-well potential (Albiez et al 2005 Phys. Rev. Lett. 95 010402) is presented, exhibiting good agreement.

We study stationary and dynamical properties of the many-body Landau-Zener dynamics of a Bose quantum fluid confined in two coupled one-dimensional chains, using a many-body generalization recently reported [Y.-A. Chen et al.], within the decoupling approximation and the one-level band scheme. The energy spectrum evidences the structure of the avoided level crossings as a function of the on-site inter particle interaction strength. On the dynamical side, a phase diagram of the transfer efficiency across ground-state and inverse sweeps is presented. A totally different scenario with respect to the original single-particle Landau-Zener scheme is found for ground-state sweeps, in which a breakdown of the adiabatic region emerges as the sweep rate decreases. On the contrary, the transfer efficiency across inverse sweeps reveals consistent results with the single-particle LandauZener predictions. In the strong coupling regime, we find that there is a critical value of the on-site interaction for which the transfer of particles starts to vanish independently of the sweep rate. Our results are in qualitative agreement with those of the experimental counterpart.

We present a thorough pedagogical analysis of the single particle localization phenomenon in a quasiperiodic lattice in one dimension. Description of disorder in the lattice is represented by the Aubry-André model. Characterization of localization is performed through the analysis of both, stationary and dynamical properties. The stationary properties investigated are the inverse participation ratio (IPR), the normalized participation ratio (NPR) and the energy spectrum as a function of the disorder strength. As expected, the distinctive Hofstadter pattern is found. Two dynamical quantities allow to discern the localization phenomenon, being the spreading of an initially localized state and the evolution of population imbalance in even and odd sites across the lattice.