Experimentally Accessible Quantum Phase Transition in a non-Hermitian Tavis-Cummings Model Engineered with Two Drive Fields

We study the quantum phase transition (QPT) in a non-Hermitian Tavis-Cummings (TC) model of experimentally accessible parameters, which is engineered with two drive fields applied to an ensemble of two-level systems (TLSs) and a cavity, respectively. When the two drive fields satisfy a given parameter-matching condition, the coupled cavity-TLS ensemble system can be described by an effective standard TC Hamiltonian in the rotating frame. In this ideal Hermitian case, the engineered TC model can exhibit the super-radiant QPT with spin conservation at an experimentally accessible critical coupling strength, but the QPT is, however, spoiled by the decoherence. We find that in this non-Hermitian case, the QPT can be recovered by introducing a gain in the cavity to balance the loss of the TLS ensemble. Also, the spin-conservation law is found to be violated due to the decoherence of the system. Our study offers an experimentally realizable approach to implementing QPT in the non-Hermitian TC model.