Perturbing the driven Dicke superradiant transition using homogenous dephasing and individual decay

The driven Dicke model, describing the collective interaction between a quantized cavity mode and a large number of two-level atoms, is predicted to exhibit a superradiant phase transition when the coupling strength is beyond a critical value. Kirton and Keeling [1] showed that an infinitesimal amount of homogeneous dephasing will destroy the transition and the addition of individual atom decay will restore it. In this work, we investigate this problem from the view of degenerate perturbation theory. The homogeneous dephasing and individual decay perturb the driven Dicke model and mix the steady states with different total spins. A coupling matrix is constructed to show the mixing effect, and its null vector shows the probability distribution of the new steady state on each total spin subspace. We also tune the fraction of contribution from these two kinds of perturbations and study how this modulates the probability distribution.

[1] P. Kirton and J. Keeling, Suppressing and restoring the Dicke superradiance transition by dephasing and decay, Phys. Rev. Lett. 118, 123602 (2017).