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arXiv:cond-mat/0605751 · Physical Review A

Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations

Frédéric Chevy

Published Dec 29, 2006• 416 citations
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Abstract

We present a theoretical interpretation of a recent experiment presented by Zwierlein et al. [Nature (London) 442, 54 (2006)] on the density profile of Fermi gases with unbalanced spin populations. We show that in the regime of strong interaction, the boundaries of the three phases observed by Zwierlein et al. can be characterized by two dimensionless numbers ${\ensuremath{\eta}}_{\ensuremath{\alpha}}$ and ${\ensuremath{\eta}}_{\ensuremath{\beta}}$. Using a combination of a variational treatment and a study of the experimental results, we infer rather precise bounds for these two parameters.

DOI
10.1103/physreva.74.063628

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We present a theoretical interpretation of a recent experiment presented by Zwierlein et al. [Nature (London) 442, 54 (2006)] on the density profile of Fermi gases with unbalanced spin populations. We show that in the regime of strong interaction, the boundaries of the three phases observed by Zwierlein et al. can be characterized by two dimensionless numbers \ensuremathη\ensuremathα{\ensuremath{\eta}}_{\ensuremath{\alpha}}\ensuremathη\ensuremathα​ and \ensuremathη\ensuremathβ{\ensuremath{\eta}}_{\ensuremath{\beta}}\ensuremathη\ensuremathβ​. Using a combination of a variational treatment and a study of the experimental results, we infer rather precise bounds for these two parameters.
We obtain the phase diagram of spin-imbalanced interacting Fermi gases from measurements of density profiles of 6Li^{6}\mathrm{Li}6Li atoms in a harmonic trap. These results agree with, and extend, previous experimental measurements. Measurements of the critical polarization at which the balanced superfluid core vanishes generally agree with previous experimental results and with quantum Monte Carlo (QMC) calculations in the Bardeen-Cooper-Schrieffer and unitary regimes. We disagree with the QMC results in the Bose-Einstein condensate regime, however, where the measured critical polarizations are greater than theoretically predicted. We also measure the equation of state in the crossover regime for a gas with equal numbers of the two fermion spin states.
We map out the detailed phase diagram of a trapped ultracold Fermi gas with population imbalance across a wide Feshbach resonance. We show that under the local density approximation, the properties of the atoms in any (anisotropic) harmonic traps are universally characterized by three dimensionless parameters: the normalized temperature, the dimensionless interaction strength, and the population imbalance. We then discuss the possible quantum phases in the trap, and quantitatively characterize their phase boundaries in various typical parameter regions.
We consider a trapped unbalanced Fermi gas at nonzero temperatures where the superfluid Sarma phase is stable. We determine, in particular, the phase boundaries between the superfluid, normal, and phase-separated regions of the trapped unbalanced Fermi mixture. We show that the physics of the Sarma phase is sufficient to understand the recent observations of Zwierlein et al. [Science 311, 492 (2006); Nature (London) 442, 54 (2006)] and indicate how the apparent contradictions between this experiment and the experiment of Partridge et al. [Science 311, 503 (2006)] may be resolved.
We consider imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mix-tures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species both occupying only a single hyperfine state. In both cases, the number of atoms for each component is allowed to be differ-ent, which leads to a spin imbalance, or spin polarization. Two different atomic species also lead to a mass imbalance. Imbalanced Fermi gases are relevant to condensed-matter physics, nuclear physics and astroparticle physics. They have been studied intensively in recent years, following their experimental realization in ultracold atomic Fermi gases. The experimental control in such a system allows for a systematic study of the equation of state and the phase diagram as a function of temperature, spin polarization and interaction strength. In this re-view, we discuss the progress in understanding strongly-interacting imbalanced Fermi gases, where a main goal is to describe the results of the highly controlled experiments. We start by discussing Feshbach resonances, after which we treat the imbalanced Fermi gas in mean-field theory to give an introduction to the relevant physics. We encounter several unusual superfluid phases, including phase-separation, gapless Sarma superfluidity, and supersolidity. To obtain a more quantitative description of the experiments, we review also more sophisti-cated techniques, such as diagrammatic methods and the renormalization-group theory. We end the review by discussing two theoretical approaches to treat the inhomogeneous imbalanced Fermi gas, namely the Landau-Ginzburg theory and the Bogoliubov-de Gennes approach. Key words: