Breakdown of Photon Blockade: A Dissipative Quantum Phase Transition in Zero Dimensions

The Jaynes-Cummings model with coherent drive is considered as an example of a nonlinear oscillator exhibiting photon blockade, where blockade by one, two, three, etc., photons occurs at a sequence of multiphoton absorption resonances. It is shown that with increasing drive strength, the blockade breaks down by way of a dissipative quantum phase transition. The transition is first order, except at a critical point in the space of drive amplitude and detuning, where a continuous transition is observed. Numerical solutions to the quantum master equation in the steady state are presented and compared with mean-field treatments based on Jaynes and Cummings' semiclassical equations (strong coupling with conserved pseudospin) and the Maxwell-Bloch equations (spontaneous emission included). The concept of a "thermodynamic limit" in the absence of conserved particle number is explored. Contrasting the identity of large photon number with weak coupling (large volume) in other dissipative quantum phase transitions for photons (e.g., in the phase-transition analogy of laser threshold), the limit of large photon numbers is a strong-coupling limit.