Exact Treatment of Spin-Orbit Coupled Bosons in an Optical Ring Cavity

Confining ultracold atoms in optical ring cavities can yield synthetic magnetic fields and spin-orbit coupling (SOC). Previous mean-field calculations showed that the interplay of the cavity-mediated long-ranged interactions and SOC can stabilize novel states, such as a stripe phase, but the strength of the SOC is limited by the usual continuum atomic recoil momentum. We investigate this system for small numbers of atoms and photons using exact diagonalization. We find that the ground state is significantly different from the mean-field approximation, in particular characterized by large entanglement. Furthermore, the system can be constructed so that the effective SOC persists for much higher atom-photon coupling strengths than can be obtained in the continuum.