The fate of the Fermi surface coupled to a single-wave-vector cavity mode

TL;DR

This paper investigates how a single-wave-vector cavity mode affects a Fermi gas, revealing competing instabilities and Fermi surface deformations, with implications for ultracold atom experiments.

Contribution

It provides a full solution to the competing instabilities induced by cavity-mediated interactions in a Fermi gas, including density-wave and superfluid phases.

Findings

Density-wave instability dominates with attractive interactions.

Repulsive interactions favor non-superradiant superfluid phases.

Fermi surface is always deformed from isotropic shape regardless of instabilities.

Abstract

The electromagnetic field of standing-wave or ring cavities induces a spatially modulated, infinite-range interaction between atoms in an ultracold Fermi gas, with a single wavelength comparable to the Fermi length. This interaction has no analog in other systems of itinerant particles and has so far been studied only in the regime where it is attractive at zero distance. Here, we fully solve the problem of competing instabilities of the Fermi surface induced by single-wavelength interactions. We find that while the density-wave (superradiant) instability dominates on the attractive side, it is absent for repulsive interactions, where the competition is instead won by non-superradiant superfluid phases at low temperatures, with Fermion pairs forming at both vanishing and finite center-of-mass momentum. Moreover, even in the absence of such symmetry-breaking instabilities, we find the Fermi surface to be always nontrivially deformed from an isotropic shape. We estimate this full phenomenology to be within reach of dedicated state-of-the-art experimental setups.