Fate of photon blockade in the deep strong coupling regime
  We investigate the photon emission properties of the driven-dissipative Rabi model in the so-called ultrastrong and deep strong coupling regimes, where the atom-cavity coupling rate $g$ becomes comparable or larger than the cavity frequency $\omega_c$. By solving numerically the master equation in the dressed-state basis, we compute the output field correlation functions in the steady-state for a wide range of coupling rates. We find that, as the atom-cavity coupling strength increases, the system undergoes multiple transitions in the photon statistics. In particular, a first sharp anti-bunching to bunching transition, occurring at $g\sim0.45\omega_c$, leading to the breakdown of the photon blockade due to the counter-rotating terms, is shown to be the consequence of a parity shift in the energy spectrum. A subsequent revival of the photon blockade and the emergence of the quasi-coherent statistics, for even larger coupling rates, are attributed to an interplay between the nonlinearity in the energy spectrum and the transition rates between the dressed states. 
Alexandre Le Boit\'e, Myung-Joong Hwang, Hyunchul Nha, Martin B.   Plenio
quant-ph