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arXiv:cond-mat/0605039 · Physical Review Letters

Intermediate-Temperature Superfluidity in an Atomic Fermi Gas with Population Imbalance

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

Published Sep 1, 2006• 73 citations
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Abstract

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."

DOI
10.1103/physrevlett.97.090402

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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."
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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.
We determine the superfluid transition temperature Tc{T}_{c}Tc​ and related finite temperature phase diagrams for the entire BCS--Bose-Einstein-condensation crossover in a three-dimensional homogeneous mixture of 6Li^{6}\text{L}\text{i}6Li and 40K^{40}\text{K}40K atoms with population imbalance. Our work is motivated by the recent observation of an interspecies Feshbach resonance. Pairing fluctuation effects, which significantly reduce Tc{T}_{c}Tc​ from the onset temperature for pairing $({T}^{\ensuremath{\ast}})$, provide reasonable estimates of Tc{T}_{c}Tc​ 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.
A detailed description is given of the phase diagram for a two-component unitary Fermi gas with mass and population imbalance, for both homogeneous and trapped systems. This aims at providing quantitative benchmarks for the normal-to-superfluid phase transition of a mass-imbalanced Fermi gas in the temperature-polarization parameter space. A self-consistent ttt-matrix approach is adopted, which has already proven to accurately describe the thermodynamic properties of the mass- and population-balanced unitary Fermi gas. Our results provide a guideline for the ongoing experiments on heteronuclear Fermi mixtures.
an atomic mass in the -component) in the BCS-BEC crossover region. Including pairing fluctuations within a self-consistent T -matrix theory, we examine how the superfluid instability is affected by the presence of mass imbalance. We determine the superfluid region in the phase diagram of a Fermi gas in terms of the temperature, the strength of a pairing interaction, and the ratio of mass imbalance. The superfluid phase transition is shown to always occur even when m m#. 2 This behavior of Tc is quite different from the previous result in an extended T -matrix theory, 3 where Tc vanishes at a certain value of m=m# > 0 in the BCS regime. Since Fermi condensates with mass imbalance have been discussed in various systems, such as a cold Fermi gas, an exciton(polariton) condensate, as well as color superconductivity, our results would be useful for further understandings of these novel Fermi superfluids.
We present phase diagrams for population-imbalanced, trapped Fermi superfluids near unitarity. In addition to providing quantitative values for the superfluid transition temperature, the pairing onset temperature, and the transition line (separating the Sarma and phase separation regimes), we study experimental signatures of these transitions based on density profiles and density differences at the center. Predictions on the BCS side of resonance show unexpected behavior, which should be searched for experimentally.