# Antiferromagnetic self-ordering of a Fermi gas in a ring cavity

## TL;DR

This paper investigates how a Fermi gas of spin-1/2 atoms self-organizes into antiferromagnetic and density-ordered states within a ring cavity, revealing symmetry-breaking superradiant phases and cavity-mediated fermionic correlations.

## Contribution

It demonstrates the emergence of antiferromagnetic self-ordering and novel fermionic correlations in a driven Fermi gas coupled to a ring cavity, highlighting symmetry-breaking phase transitions.

## Key findings

- Antiferromagnetic lattice order at cavity wavelength.
- Spontaneous breaking of U(1) and Z2 symmetries at superradiance.
- Positive momentum pair correlations between opposite spins.

## Abstract

We explore the density and spin self-ordering of driven spin-$1/2$ collisionless fermionic atoms coupled to the electromagnetic fields of a ring resonator. The two spin states are two-photon Raman-coupled via a pair of degenerate counterpropagating cavity modes and two transverse pump fields. In this one-dimensional configuration the coupled atom-field system possesses a continuous $U(1)$ translational symmetry and a discrete $\mathbf{Z}_2$ spin inversion symmetry. At half filling for sufficiently strong pump strengths, the combined $U(1)\times \mathbf{Z}_2$ symmetry is spontaneously broken at the onset of a superradiant phase transition to a state with self-ordered density and spin structures. We predominately find an antiferromagnetic lattice order at the cavity wavelength. The self-ordered states exhibit unexpected positive momentum pair correlations between fermions with opposite spin. These strong cavity-mediated correlations vanish at higher pump strength.