The zero-temperature phase diagrams of imbalanced two-species Fermi gases are investigated in asymmetric optical lattices with arbitrary potential depths, based on the exact spectrum instead of the Fermi-Hubbard model. We study the effect of lattice potentials and atomic densities to the fully paired Bardeen-Cooper-Schrieffer (BCS) state and particularly the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. It is found that the increasing lattice potential favors BCS at low densities because of the enhanced effective coupling, whereas FFLO is favored at intermediate densities when the system undergoes a dimensional crossover. Finally, using the local density approximation, we study the evolution of the phase profile in the presence of external harmonic traps by merely tuning the lattice potentials.
The zero-temperature phase diagrams of imbalanced two-species Fermi gases are investigated in asymmetric optical lattices with arbitrary potential depths, based on the exact spectrum instead of the Fermi-Hubbard model. We study the effect of lattice potentials and atomic densities to the fully paired Bardeen-Cooper-Schrieffer (BCS) state and particularly the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. It is found that the increasing lattice potential favors BCS at low densities because of the enhanced effective coupling, whereas FFLO is favored at intermediate densities when the system undergoes a dimensional crossover. Finally, using the local density approximation, we study the evolution of the phase profile in the presence of external harmonic traps by merely tuning the lattice potentials.
We investigate a one-dimensional two-component system in an optical lattice of attractive interactions under a spin-dependent external potential. Based on the density-matrix renormalization group methods, we obtain its phase diagram as a function of the external potential imbalance and the strength of the attractive interaction through the analysis on the density profiles and the momentum pair correlation functions. We find that there are three different phases in the system, a coexisted fully polarized and Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase, a normal polarized phase, and a Bardeen–Cooper–Schrieffer (BCS) phase. Different from the systems of spin-independent external potential, where the FFLO phase is normally favored by the attractive interactions, in the present situation, the FFLO phases are easily destroyed by the attractive interactions, leading to the normal polarized or the BCS phase.
We study the phase diagram of an imbalanced two-component Fermi gas in optical lattices of 1–3 dimensions (1D–3D), considering the possibilities of the Fulde–Ferrel–Larkin–Ovchinnikov (FFLO), Sarma/breached pair, BCS and normal states as well as phase separation, at finite and zero temperatures. In particular, phase diagrams with respect to average chemical potential and the chemical potential difference of the two components are considered, because this gives the essential information about the shell structures of phases that will occur in the presence of an additional (harmonic) confinement. These phase diagrams in 1D, 2D and 3D show in a striking way the effect of Van Hove singularities on the FFLO state. Although we focus on population imbalanced gases, the results are relevant also for the (effective) mass imbalanced case. We demonstrate by LDA calculations that various shell structures such as normal–FFLO–BCS–FFLO–normal, or FFLO–normal, are possible in presence of a background harmonic trap. The phases are reflected in noise correlations: especially in 1D the unpaired atoms leave a clear signature of the FFLO state as a zero-correlation area ('breach') within the Fermi sea. This strong signature occurs both for a 1D lattice as well as for a 1D continuum. We also discuss the effect of Hartree energies and the Gorkov correction on the phase diagrams.
In three-dimensional Fermi gases with spin imbalance, a competition exists between Cooper pairing with zero and finite momentum. The latter gives rise to the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superfluid phase, which only exists in a restricted area of the phase diagram as a function of chemical potential imbalance and interaction strength. Applying an optical potential along one direction enhances the FFLO region in this phase diagram. In this paper, we construct the phase diagram as a function of polarization and interaction strength in order to study the competition between the FFLO phase and the spin balanced Bardeen–Cooper–Schrieffer (BCS) phase. This allows us to take into account the region of phase separation, and provides a more direct connection with experiment. Subsequently, we investigate the effects of the wavelength and the depth of the optical potential, which is applied along one direction, on the FFLO state. It is shown that the FFLO state can exist up to a higher level of spin imbalance if the wavelength of the optical potential becomes smaller. Our results give rise to an interesting effect: the maximal polarization at which the FFLO state can exist decreases when the interaction strength exceeds a certain critical value. This counterintuitive phenomenon is discussed and the connection to the optical potential is explained.
We present phase diagrams for a polarized Fermi gas in an optical lattice as a function of temperature, polarization, and lattice filling factor. We consider the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma or breached pair, and BCS phases, and the normal state and phase separation. We show that the FFLO phase appears in a considerable portion of the phase diagram. The diagrams have two critical points of different nature. We show how various phases leave clear signatures to momentum distributions of the atoms which can be observed after time of flight expansion.
The zero-temperature phase diagrams of imbalanced fermions in three-dimensional optical lattices are investigated to evaluate the validity of the Fermi-Hubbard model. It is found that depending on the filling factor, s-wave scattering strength, and lattice potential, the system may fall into the normal (N) phase, magnetized superfluid (SFM), or phase separation of N and Bardeen-Cooper-Schrieffer state. By tuning these parameters, the superfluidity could be favorable by enhanced effective couplings or suppressed by the increased band gap. The phase profiles in the presence of a harmonic trap are also investigated under LDA, which show some exotic shell structures compared to those without the optical lattice.
In this paper we study the superfluid density of the two component Fermi gas in optical lattices with population imbalance. Three different type of phases, the BCS-state (Bardeen, Cooper, and Schrieffer), the FFLO-state (Fulde, Ferrel, Larkin, and Ovchinnikov), and the Sarma state, are considered. We show that the FFLO superfluid density differs from the BCS/Sarma superfluid density in an important way. Although there are dynamical instabilities in the FFLO phase, when the interaction is strong or densities are high, on the weak coupling limit the FFLO phase is found to be stable.