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arXiv:0804.2705 · Physical Review A

Phase separation in a mixture of a Bose-Einstein condensate and a two-component Fermi gas as a probe of Fermi superfluidity

S. G. Bhongale, Han Pu

Published Dec 16, 2008• 12 citations
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Abstract

We study the phase diagram of the mixture of a Bose-Einstein condensate and a two-component Fermi gas. In particular, we identify the regime where the homogeneous system becomes unstable against phase separation. We show that, under proper conditions, the phase-separation phenomenon can be exploited as a robust probe of ``local'' Fermi superfluidity.

DOI
10.1103/physreva.78.061606

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We study the phase diagram of the mixture of a Bose-Einstein condensate and a two-component Fermi gas. In particular, we identify the regime where the homogeneous system becomes unstable against phase separation. We show that, under proper conditions, the phase-separation phenomenon can be exploited as a robust probe of ``local'' Fermi superfluidity.
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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.
Trapped ultra-cold atom experiments provide a unique opportunity to understand Bose-Fermi superfluid mixtures occurring in contrasting areas of physics. At present there are several atom-trap experiments that could potentially explore this superfluid-mixture regime, thus warranting a detailed understanding of the occurrence and stability of various possible thermodynamic phases in the mixture. In the present work, we therefore construct the finite temperature phase diagram of an interacting atomic mixture of Bose and Fermi superfluids. Our study reveals a unique region of phase space, where the BCS instability of the Fermi surface coincides with dynamical instability of the homogeneous mixture towards phase separation through a first-order transition. We illustrate how this intriguing interplay manifests in a trapped configuration, thereby providing important constraints for observing superfluidity in experiments.
We consider a system of repulsively interacting Bose-Fermi mixtures of spin-polarized uniform atomic gases at zero temperature. We examine possible realization of ppp-wave superfluidity of fermions due to an effective attractive interaction via density fluctuations of Bose-Einstein condensate within mean-field approximation. We find the ground state of the system by direct energy comparison of the ppp-wave superfluid state in a single uniform mixed phase and normal Fermi gas state in a phase-separated phase, and suggest an occurrence of the ppp-wave superfluidity for a strong boson-fermion interaction regime. We study some signatures of the ppp-wave superfluid, such as anisotropic energy gap and quasiparticle energy in the axial state, that have not been observed in spin-unpolarized superfluid of atomic fermions. We also show that a Cooper pair is a tightly bound state, such as a diatomic molecule in the strong boson-fermion coupling regime, and suggest an observable indication of the ppp-wave superfluid in the real experiment.
We probe the interface between a phase-separated Bose-Fermi mixture consisting of a small Bose-Einstein condensate of ^{41}K residing in a large Fermi sea of ^{6}Li. We quantify the residual spatial overlap between the two components by measuring three-body recombination losses for variable strength of the interspecies repulsion. A comparison with a numerical mean-field model highlights the importance of the kinetic energy term for the condensed bosons in maintaining the thin interface far into the phase-separated regime. Our results demonstrate a corresponding smoothing of the phase transition in a system of finite size.