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

The many-body physics of higher-spin systems is expected to host qualitatively new matter phases, but realizing them requires the controllable multispin interactions that can be tuned independently for each spin component. Here we propose a scheme that meets this demand in ultracold Fermi gases. By engineering the atom-cavity coupling, we generate cavity-mediated effective interactions between arbitrary pseudo-spin states. Focusing on the simplest three-spin case, we obtain two independent scattering channels whose strengths and signs can be adjusted separately. The resulting Hamiltonian combines the on-site attraction 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 space of a higher-spin representation, rather than in the density profile. The proposal is reliable to be implemented using the existing techniques of ultracold atoms. Therefore it offers a versatile platform for quantum simulation of higher-spin many-body physics.