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.
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.
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