Thermodynamics of Trapped Imbalanced Fermi Gases at Unitarity

Abstract

We present a theory for the low-temperature properties of a resonantly interacting Fermi mixture in a trap, that goes beyond the local-density approximation. The theory corresponds essentially to a Landau-Ginzburg-like approach that includes self-energy effects to account for the strong interactions at unitarity. We show diagrammatically how these self-energy effects arise from fluctuations in the superfluid order parameter. Gradient terms of the order parameter are included to account for inhomogeneities. This approach incorporates the state-of-the-art knowledge of the homogeneous mixture with a population imbalance exactly and gives good agreement with the experimental density profiles of Shin et al. [Nature 451, 689 (2008)]. This allows us to calculate the universal surface tension of the interface between the equal-density superfluid and the partially polarized normal state of the mixture. We also discuss the possibility of a metastable state to explain the deformation of the superfluid core that is seen in the experiment of Partridge et al. [Science 311, 503 (2006)].

26 pages, 7 figures, contribution to Lecture Notes in Physics "BCS-BEC crossover and the Unitary Fermi Gas" edited by W. Zwerger

References in corpus (11)

• Phase diagram of a two-component Fermi gas with resonant interactions
• Normal state of a polarized Fermi gas at unitarity
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• A Unitary Fermi Supersolid: The Larkin-Ovchinnikov Phase
• Surface Tension in Unitary Fermi Gases with Population Imbalance
• Polarization Measurements and the Pairing Gap in the Universal Regime
• Renormalization Group Theory for the Imbalanced Fermi Gas
• Lifshitz Point in the Phase Diagram of Resonantly Interacting ${}^{6}Li$-${}^{40}K$ Mixtures
• Concomitant Modulated Superfluidity In Polarized Fermionic Gases
• Inhomogeneous Fermi mixtures at Unitarity: Bogoliubov-de Gennes vs. Landau-Ginzburg

Cited by in corpus (1)

• The Unitary Fermi Gas: From Monte Carlo to Density Functionals