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arXiv:cond-mat/0607803 · Annals of Physics

BEC–BCS crossover, phase transitions and phase separation in polarized resonantly-paired superfluids

Daniel E. Sheehy, Leo Radzihovsky

Published Nov 22, 2006• 211 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2006.09.009

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We study resonantly-paired s-wave superfluidity in a degenerate gas of two species (hyperfine states labeled by ↑, ↓) of fermionic atoms when the numbers N↑ and N↓ of the two species are unequal, i.e., the system is "polarized." We find that the continuous crossover from the Bose-Einstein condensate (BEC) limit of tightly-bound diatomic molecules to the Bardeen-Cooper-Schrieffer (BCS) limit of weakly correlated Cooper pairs, studied extensively at equal populations, is interrupted by a variety of distinct phenomena under an imposed population difference ΔN ≡ N↑ - N↓. Our findings are summarized by a "polarization" (ΔN) versus Feshbach-resonance detuning (δ) zero-temperature phase diagram, which exhibits regions of phase separation, a periodic FFLO superfluid, a polarized normal Fermi gas and a polarized molecular superfluid consisting of a molecular condensate and a fully polarized Fermi gas. We describe numerous experimental signatures of such phases and the transitions between them, in particular focusing on their spatial structure in the inhomogeneous environment of an atomic trap. © 2006 Elsevier Inc. All rights reserved.
We map out the detuning-magnetization phase diagram for a magnetized (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an s-wave Feshbach resonance (FR). The phase diagram is dominated by the coexistence of a magnetized normal gas and a singlet-paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced FR detuning. On the BCS side of strongly overlapping Cooper pairs, a sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized phase intervenes between the phase-separated and normal states. In contrast, for large negative detuning a uniform, polarized superfluid, that is, a coherent mixture of singlet Bose-Einstein-condensed molecules and fully magnetized single-species Fermi sea, is a stable ground state.
We discuss the BCS-BEC crossover in a degenerate Fermi gas of two hyperfine states interacting close to a Feshbach resonance. We show that, by including fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink, the character of the superfluid phase transition continuously changes from the BCS-type to the BEC-type, as the threshold of the quasimolecular band is lowered. In the BEC regime, the superfluid phase transition is interpreted in terms of molecules associated with both the Feshbach resonance and Cooper pairing.