Two-band description of resonant superfluidity in atomic Fermi gases

Lianyi He, Hui Hu, and Xia-Ji Liu
Phys. Rev. A 91, 023622 – Published 23 February 2015

Abstract

Fermionic superfluidity in atomic Fermi gases across a Feshbach resonance is normally described by the atom-molecule theory, which treats the closed channel as a noninteracting point boson. In this work we present a theoretical description of the resonant superfluidity in analogy to the two-band superconductors. We employ the underlying two-channel scattering model of Feshbach resonance where the closed channel is treated as a composite boson with binding energy ɛ0 and the resonance is triggered by the microscopic interchannel coupling U12. The binding energy ɛ0 naturally serves as an energy scale of the system, which has been sent to infinity in the atom-molecule theory. We show that the atom-molecule theory can be viewed as a leading-order low-energy effective theory of the underlying fermionic theory in the limit ɛ0 and U120, while keeping the phenomenological atom-molecule coupling finite. The resulting two-band description of the superfluid state is in analogy to the BCS theory of two-band superconductors. In the dilute limit ɛ0, the two-band description recovers precisely the atom-molecule theory. The two-band theory provides a natural approach to study the corrections because of a finite binding energy ɛ0 in realistic experimental systems. For broad and moderate resonances, the correction is not important for current experimental densities. However, for extremely narrow resonance, we find that the correction becomes significant. The finite binding energy correction could be important for the stability of homogeneous polarized superfluid against phase separation in imbalanced Fermi gases across a narrow Feshbach resonance.

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  • Received 30 October 2014

DOI:https://doi.org/10.1103/PhysRevA.91.023622

©2015 American Physical Society

Authors & Affiliations

Lianyi He1, Hui Hu2, and Xia-Ji Liu2

  • 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
  • 2Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122, Australia

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Issue

Vol. 91, Iss. 2 — February 2015

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