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 (BP), 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.PACS numbers: 03.75. Ss, 03.75.Hh,74.25.Dw Recent advances in the experiments of ultracold Fermi gases have shown great potential for elucidating longstanding problems in many different fields of physics related to strongly correlated Fermions. For instance, in recent experiments [1,2,3,4,5] spin-density imbalanced, or polarized, Fermi gases were considered. Such systems make it possible to study pairing with mismatched Fermi surfaces, potentially leading to non-standard phases such as that appearing in FFLO-states [6,7] or BP-states [8] (Sarma-states). These possibilities have been considered extensively in condensed-matter, nuclear, and highenergy physics [9]. The experiments in trapped gases have shown clear evidence of the separation of the gas into a BCS core region and a normal state shell around it, i.e. phase separation. Although an FFLO-type state has been predicted to appear in these systems as well [10,11], it is likely to be difficult to observe since it appears in the edges of the trap except for large polarizations.Recent experiments [12,13] on Fermi gases confined in optical lattices have already demonstrated the potential of these systems for a multitude of studies of new phases, dimensionality effects, and dynamics. In this letter, we calculate the phase diagram for an attractively interacting Fermi gas in an optical lattice at zero and finite temperatures. In particular, we consider the possibility of the single mode FFLO-phase, where the order parameter is space-dependent, and of the BCS-BP phase, where compared to the standard BCS phase the excess polarization is carried by additional Bogoliubov excitations. We investigate their competition with the phase separation (PS) of the gas into normal and BCS superfluid regions. Our results reveal that a typical phase diagram as a function of polarization and temperature is as shown in Fig. 1: phase separation is expected for small polarizations and temperatures, whereas at zero temperature the FFLO state appears after some critical polarization. At a finite temperature, the FFLO-phase competes with the BCS-BP phase. As the temperature increases the BCS-BP phase becomes energetically favorable, and as the temperature is increased even further the BCS-BP phase gives way to a normal polarized Fermi gas.Furthermore, the phase diagrams reveal a Lifshitz point which is surrounded by the normal, FFLO, and BCS-BP phases. The transitions around this point are of second order, but the FFLO ph...

We study the phase diagram of an imbalanced two-component Fermi gas in optical lattices of 1-3 dimensions, considering the possibilities of the 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 presence of an additional (harmonic) confinement. These phase diagrams in 1, 2 and 3 dimensions 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.

We consider pairing in a three-component gas of degenerate fermions. In particular, we solve the finite temperature mean-field theory of an interacting gas for a system where both interaction strengths and fermion masses can be unequal. At zero temperature we find a a possibility of a quantum phase transition between states associated with pairing between different pairs of fermions. On the other hand, finite temperature behavior of the three-component system reveals some qualitative differences from the two-component gas: for a range of parameters it is possible to have two different critical temperatures. The lower one corresponds to a transition between different pairing channels, while the higher one corresponds to the usual superfluid-normal transition. We discuss how these phase transitions could be observed in ultracold gases of fermionic atoms.

We study the properties of a trapped interacting three component Fermi gas. We assume that one of the components can have a different mass from the other two. We calculate the different phases of the three component mixture and find a rich variety of different phases corresponding to different pairing channels, and simple ways of tuning the system from one phase to another. In particular, we predict coexistence of several different superfluids in the trap, forming a shell structure, and phase transitions from this mixture of superfluids to a single superfluid when the system parameters or temperature is varied. Such shell structures realize superfluids with a nontrivial spatial topology and leave clear observable signatures in the density profile of the gas.