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arXiv:0812.3121 · Physical Review A

Finite-temperature behavior of an interspecies fermionic superfluid with population imbalance

Hao Guo, Chih-Chun Chien, Qijin Chen, Yan He, Kathryn Levin

Published Jul 9, 2009• 20 citations
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Abstract

We determine the superfluid transition temperature ${T}_{c}$ and related finite temperature phase diagrams for the entire BCS--Bose-Einstein-condensation crossover in a three-dimensional homogeneous mixture of $^{6}\text{L}\text{i}$ and $^{40}\text{K}$ atoms with population imbalance. Our work is motivated by the recent observation of an interspecies Feshbach resonance. Pairing fluctuation effects, which significantly reduce ${T}_{c}$ from the onset temperature for pairing $({T}^{\ensuremath{\ast}})$, provide reasonable estimates of ${T}_{c}$ and indicate that the interspecies superfluid phase should be accessible in future experiments. Although a homogeneous polarized superfluid is not stable in the ground state near unitarity, our phase diagrams show that it stabilizes at finite temperature.

DOI
10.1103/physreva.80.011601

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Superfluidity in atomic Fermi gases with population imbalance has recently become an exciting research focus. There is considerable disagreement in the literature about the appropriate stability conditions for states in the phase diagram throughout the BCS to Bose-Einstein condensation crossover. Here we discuss these stability conditions for homogeneous polarized superfluid phases, and compare with recent alternative proposals. The requirement of a positive second-order partial derivative of the thermodynamic potential with respect to the fermionic excitation gap $\ensuremath{\Delta}$ (at fixed chemical potentials) is demonstrated to be equivalent to the positive definiteness of the particle number susceptibility matrix. In addition, we show the positivity of the effective pair mass constitutes another nontrivial stability condition. These conditions determine the (local) stability of the system towards phase separation (or other ordered phases). We also study systematically the effects of finite temperature and the related pseudogap on the phase diagrams defined by our stability conditions.
In this paper we present a very general theoretical framework for addressing fermionic superfluids over the entire range of BCS to Bose Einstein condensation (BEC) crossover in the presence of population imbalance or spin polarization. Our emphasis is on providing a theory which reduces to the standard zero temperature mean-field theories in the literature, but necessarily includes pairing fluctuation effects at nonzero temperature within a consistent framework. Physically, these effects are associated with the presence of preformed pairs (or a fermionic pseudogap) in the normal phase, and pair excitations of the condensate, in the superfluid phase. We show how this finite TTT theory of fermionic pair condensates bears many similarities to the condensation of point bosons. In the process we examine three different types of condensate: the usual breached pair or Sarma phase and both the one- and two-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states. The last of these has been discussed in the literature albeit only within a Landau-Ginzburg formalism, generally valid near Tc{T}_{c}Tc​. Here we show how to arrive at the two-plane-wave LOFF state in the ground state as well as at general temperature TTT.
We derive the underlying finite temperature theory which describes Fermi gas superfluidity with population imbalance in a homogeneous system. We compute the pair formation temperature, superfluid transition temperature Tc, and superfluid density in a manner consistent with the standard ground state equations and, thereby, present a complete phase diagram. Finite temperature stabilizes superfluidity, as manifested by two solutions for Tc or by low T instabilities. At unitarity, the polarized state is an "intermediate-temperature superfluid."
The pairing and superfluid phenomena in a two-component Fermi gas can be strongly affected by the population and mass imbalances. Here we present phase diagrams of an atomic Fermi-Fermi mixture as they undergo BCS--Bose-Einstein condensation (BEC) crossover using a pairing fluctuation theory. We focus on the finite temperature and trap effects, with an emphasis on the mixture of 6{}^{6}6Li and 40{}^{40}40K. We show that there exist exotic types of phase separation in the (near-)BEC regime, associated with a pseudogap effect. Moreover, in the BCS and unitary regimes, the spatial density and gap profiles exhibit sandwichlike shell structures with superfluid or pseudogapped normal state in the middle shell. Such a sandwichlike shell structure appears when the mass imbalance increases beyond a certain threshold. Our result is relevant to future experiments on the 6{}^{6}6Li-40{}^{40}40K and other possible Fermi-Fermi mixtures.
We study the finite temperature TTT behavior of trapped Fermi gases as they undergo BCS--Bose-Einstein condensation (BEC) crossover, in the presence of a population imbalance. Our results, in qualitative agreement with recent experiments, show how the superfluid phase transition is directly reflected in the particle density profiles. We demonstrate that at $T\ensuremath{\ne}0$ and in the near-BEC and unitary regimes, the polarization is excluded from the superfluid core. Importantly, a substantial polarization fraction is carried by a normal region of the trap having strong pair correlations, which we associate with noncondensed pairs or the ``pseudogap phase.''
We study s-wave pairing of population imbalanced Fermi atoms in quasi two dimensions using a mean field theory. At zero temperature, we map out the phase diagram in the entire Bardeen, Cooper and Schrieffer-Bose Einstein condensation (BCS-BEC) crossover region by investigating the effect of weak atom tunneling between layers. We find that the superfluid phase stabilizes as one decreases the atom tunneling between layers. This allows one to control the superfluid-normal first order phase transition by tuning a single experimental parameter. Further, we find that a tunneling induced polarized superfluid phase appears in a narrow parameter region in the BEC regime. At Finite temperatures, we use a Landau-Ginzberg functional approach to investigate the possibility of spatially inhomogeneous Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in the weakly interacting BCS limit near the tricritical point of spatially homogenous superfluid, FFLO, and normal phases. We find that the normal-FFLO phase transition is first order transition as opposed to the continues transition predicted in zero temperature theories.