Dissipative phase transition in an open Tavis–Cummings model with a two-photon drive

Abstract

We investigate the steady-state quantum phases and associated collective phenomena of an open Tavis-Cummings (TC) model driven by a two-photon source. The standard (non-dissipative) TC model describes quantum phases of an ensemble of $N_q$ two-level quantum emitters interacting with a single-mode electromagnetic field. The interplay among coherent driving, dissipation, and dipole interactions of the open TC model results in emergent collective phenomena, leading to a dissipative or nonequilibrium phase transition from normal to superradiant phase. We solve the Liouvillian equation analytically using the semi-classical mean-field approximation. We carry out the stability analysis of the steady-state phases and determine the phase boundary. The use of Holstein-Primakoff transformation in the thermodynamic limit $N_q\rightarrow\infty$ reduces the system to an effective coupled-oscillator model, the solution of which yields collective modes.