Dissipative quantum phase transition in a biased Tavis-Cummings model

We study the dissipative quantum phase transition(QPT)in a biased Tavis–Cummings model consisting of an ensemble of two-level systems(TLSs)interacting with a cavity mode,where the TLSs are pumped by a drive field.In our proposal,we use a dissipative TLS ensemble and an active cavity with effective gain.In the weak drive-field limit,the QPT can occur under the combined actions of the loss and gain of the system.Owing to the active cavity,the QPT behavior can be much differentiated even for a finite strength of the drive field on the TLS ensemble.Also,we propose to implement our scheme based on the dissipative nitrogen-vacancy(NV)centers coupled to an active optical cavity made from the gainmedium-doped silica.Furthermore,we show that the QPT can be measured by probing the transmission spectrum of the cavity embedding the ensemble of the NV centers.