Cavity-induced multispin interactions and phase transitions in ultracold Fermi gases

Abstract The many-body physics of higher-spin systems is expected to host qualitatively new matter phases, but realizing them requires the controllable interactions between multispin components that can be tuned independently for each component. Here we propose a scheme that meets this demand in ultracold Fermi gases. By engineering the atom-cavity coupling, we generate cavity-induced effective interactions between pseudo-spin states via multiple Raman and cavity paths. Focusing on the simplest spin-1 case, we obtain two independent scattering channels whose relative strengths and signs are determined by the Clebsch–Gordan coefficients and optical-field parameters. The resulting Hamiltonian combines the on-site Cooper pairing with the off-site repulsion, and drives a continuous transition from the superfluid to the spin-density-wave phase. The coexistence region is reminiscent of a supersolid, yet the self-organized modulation appears in the spin density profile of a higher-spin representation, rather than in the number density profile. The proposal can be implemented with the existing techniques in ultracold atoms. Therefore it offers a versatile platform for quantum simulation of higher-spin many-body physics.