Finite-Temperature Phase Diagram of a Polarized Fermi Gas in an Optical Lattice

Abstract

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...

Fulde-Ferrell-Larkin-Ovchinnikov state in the dimensional crossover between one- and three-dimensional lattices

“…In the 3D limit, we find that the FFLO state is broken near local polarization 0.35 at a trap center that is approximately a quarter filled, which contrasts to the mean-field values ∼0.6 (|U | = 5.14) 8 and ∼0.75 (|U | = 6) 9 at the same filling. This enhancement of the normal state can be understood in light of the fact that including the particle-hole channel was shown to reduce pairing significantly in lattices: 28 DMFT includes full local quantum fluctuations, causing such higher order effects.…”

“…A comparison with the previous mean-field results in 1D and 3D lattices shows the drastic effects of local quantum fluctuations: (1) Our results indicate that the large size of the FFLO area predicted by mean-field theory in 3D lattices 8,9 may have been overestimated. In the 3D limit, we find that the FFLO state is broken near local polarization 0.35 at a trap center that is approximately a quarter filled, which contrasts to the mean-field values ∼0.6 (|U | = 5.14) 8 and ∼0.75 (|U | = 6) 9 at the same filling.…”

“…One peculiar feature of this exotic phase is that apparently its stability is largely affected by the dimensionality of the system. It turns out that the three-dimensional (3D)-FFLO state occupies a thin area of the mean-field phase diagram, 7 though the signature can be stronger in systems that support nesting such as optical lattices 8,9 and elongated traps. 10 Indeed, only phase separation was observed for ultracold gases in 3D traps.…”

FFLO order in ultra-cold atoms in three-dimensional optical lattices

“…However, in most cases these studies were limited to targeted states, fixed size simulation cells or to one-and two-dimensional lattices [8][9][10][11][12]. Three-dimensional lattices are in many ways the most direct and natural for optical lattice experiments with ultra-cold atomic gases, so these systems offer the most realistic possibility of observing FFLO states.…”

Collective modes and the speed of sound in the Fulde-Ferrell-Larkin-Ovchinnikov state

“…We concentrate on two-component spin-imbalanced Fermi gases at finite temperature in the lowest band of a two-dimensional (2D) or a quasi-1D optical lattice and with an on-site interaction. The optical lattice is motivated by theoretical studies, indicating that the lattice aids the formation of the FFLO state as the lattice dispersion improves the overlap between the Fermi surfaces of the majority and minority components [31,32]. Our method for calculating the collective mode spectrum is based on the generalized random-phase approximation (GRPA) for the linear response function of the system.…”