Superfluid fraction and Leggett bound in a density-modulated strongly interacting Fermi gas at zero temperature

Year: 2024

Authors: Orso G., Stringari S.

Autors Affiliation: Univ Paris Cite, Lab Mateeriaux & Pheenomenes Quant MPQ, CNRS, F-75013 Paris, France; Univ Trento, Pitaevskii BEC Ctr, CNR INO, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, Via Sommar 14, I-38123 Trento, Italy.

Abstract: We calculate the superfluid fraction of an interacting Fermi gas, in the presence of a one-dimensional periodic potential of strength V-0 and wave vector q. Special focus is given to the unitary Fermi gas, characterized by the divergent behavior of the s-wave scattering length. Comparison with the Leggett’s upper bound (< n(1D)><1/n(1D)>)(-1), with n(1D )the one-dimensional column density, explicitly shows that differently from the case of a dilute interacting Bose gas, the bound significantly overestimates the value of the superfluid fraction, except in the phonon regime of small q. Sum rule arguments show that the combined knowledge of the Leggett bound and of the actual value of the superfluid fraction allows for the determination of curvature effects, providing the deviation of the dispersion of the Anderson-Bogoliubov mode from the linear phonon dependence. The comparison with the predictions of the weakly interacting BCS Fermi gas points out the crucial role of two-body interactions. The implications of our predictions on the anisotropic behavior of the sound velocity are also discussed.

Journal/Review: PHYSICAL REVIEW A

Volume: 109 (2)      Pages from: 23301-1  to: 23301-9

More Information: We thank Y. Castin, F. Dalfovo, S. Giorgini, A. Leggett, and W. Zwerger for fruitful discussions. This work was granted access to the HPC resources of TGCC under the allocations AD010513635 and AD010513635R1 supplied by GENCI (Grand Equipement National de Calcul Intensif) . S.S. acknowledges continuous financial support from PAT (Provincia Autonoma di Trento) .
KeyWords: 2nd Sound
DOI: 10.1103/PhysRevA.109.023301

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