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

Abstract

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