Unbound-to-bound transition of two-atom polaritons in an optical cavity

We consider two spin-1/2 fermions inside an optical cavity which supports a single-mode quantized light field. We demonstrate that the atom-light coupling (ALC) gives rise to the two-atom polariton states, where the two atoms are highly entangled with cavity photons. We focus on the case where the cavity light is on resonant with the bare atomic transition. We show that in the absence of interatomic interaction, the polariton is unbound, has finite center-of-mass momentum, and contains no atomic spin-singlet fraction in its ground state. When strong attractive interatomic contact interaction is present, a stable bound polariton state exists when the ALC strength is below a critical value. When the ALC strength exceeds the critical value, a first-order transition is observed and the bound polariton becomes unbound. The first-order transition is characterized by abrupt changes of various quantities associated with the polariton and should be readily detectable.