Open questions for strongly interacting Fermi gases with zero-range interactions

TL;DR

This paper reviews unresolved theoretical issues in three-dimensional strongly interacting Fermi gases near Feshbach resonances, focusing on few-body, low-energy effective, and many-body problems with implications for cold atom experiments.

Contribution

It identifies key open questions across different theoretical frameworks in strongly interacting Fermi gases, highlighting areas needing further research.

Findings

Stability of the gas against Efimov effect

Damping of phonon modes and condensate coherence

Properties of collective excitations like Goldstone and Higgs modes

Abstract

We review some unresolved theoretical issues in three-dimensional two-component Fermi gases, drawing on recent experiments on cold atoms in immaterial traps close to a magnetic Feshbach resonance. We distinguish successively (i) the open questions arising in the few-body problem with Wigner-Bethe-Peierls contact interactions - essentially the stability of the gas with respect to the Efimov effect and the calculation of the cluster (or virial) coefficients, (ii) those arising in the effective low-energy theory of Landau and Khalatnikov quantum hydrodynamics - essentially the damping of phonon modes and the coherence time of the condensate of pairs, and finally (iii) questions requiring a complete, microscopic solution of the many-body problem, such as the specific properties of the acoustic excitation branch (Goldstone) of the condensate of pairs, or its collective excitation branch (Higgs) in the broken-pair continuum.