Replica symmetry breaking in multimode cavity QED

We numerically demonstrate that an interacting atomic spin system coupled via a multimode optical cavity can enter a spin glass regime with replica symmetry breaking (RSB). Multimode optical cavities support many degenerate transverse modes that can mediate all-to-all sign-changing spin interactions. Such a system realizes an approximate, disordered Ising model with a transverse field. We simulate the pumping of the system through the Ising transition and study individual replicas as quantum trajectories monitored under continuous measurement. A Parisi-like overlap distribution is found from the RSB that emerges via dissipation.