Stability of many-body localization in cavity QED with photon loss

Over the past decade, an extensive number of works predicted that for strong enough disorder, certain interacting closed quantum systems (specifically 1D) could avoid thermalization due to many-body localization (MBL). On the other hand, in open quantum systems, the coherent non-ergodic behavior is destroyed by decoherence from the bath; thus, MBL does not usually survive in such scenarios. We argued in recent works that MBL is accessible in cavity quantum electrodynamics (QED) [arXiv:2208.06898, PRL 122, 240402]. Motivated by these works, we will give evidence that MBL remains stable after the inclusion of cavity loss. Using a high-frequency expansion (HFE) we show how cavity loss modifies the long-range coupling inherent to cavity QED, favoring a localized steady state rather than a featherless delocalized steady state. In addition, we attempt to track the flow of energy in different subsystems and support our analytic arguments with numerical simulations.