BCS-BCS crossover between atomic and molecular superfluids in a Bose-Fermi mixture

TL;DR

This paper presents a theoretical study of the continuous transition between atomic and molecular Fermi superfluids in a Bose-Fermi mixture near a Feshbach resonance, revealing a two-band superfluid structure with enhanced pair-exchange coupling.

Contribution

It introduces a mean-field framework based on a two-channel model, demonstrating the atom-molecule superfluid continuity and its equivalence to a two-band superconductor model.

Findings

Superfluid gaps are strongly enhanced near the Feshbach resonance.

Atomic and molecular superfluids coexist within a two-band superfluid theory.

The pair-exchange coupling can be experimentally probed via Josephson effect.

Abstract

We theoretically examine a continuity between atomic and molecular Fermi superfluids in a Bose-Fermi mixture near the Feshbach resonance. Considering a two-channel model describing the Feshbach resonance between Fermi and Bose atoms, we have constructed the mean-field framework based on the perturbative expansion of the Feshbach atom-dimer coupling. The resulting effective Hamiltonian exhibits not only the continuity between atom-atom to molecule-molecule Cooper pairings but also becomes equivalent to the two-band-superconductor model with Suhl-Matthias-Walker type pair-exchange coupling. We demonstrate how these atomic and molecular Fermi superfluids coexist within the two-band-like superfluid theory. The pair-exchange coupling and resulting superfluid gaps are found to be strongly enhanced near the Feshbach resonance due to the interplay between the infrared singularity of Bogoliubov phonons and their Landau damping arising from the coupling with fermions. The pair-exchange coupling can be probed via the observation of the intrinsic Josephson effect between atomic and molecular superfluids.