Finite-size scaling of the photon-blockade breakdown dissipative quantum phase transition.

The time evolution of a quantum system undergoing a dissipative, first-order quantum phase transition is studied. We consider the photon-blockade-breakdown phase transition, which takes place in the driven Jaynes-Cummings model with strong coupling between the two-level system and the harmonic oscillator. For a certain range of drive strength, the stationary solution corresponds to a bistability of classically distinguishable states. By unraveling the stationary solution into quantum trajectories, we resolve the nature of coexistence of phases. We show that the bistability solution develops into a first-order phase transition in the thermodynamic limit. We calculate the finite-size scaling exponent numerically. Even in the thermodynamic limit, the stability of phases originates from the discrete spectrum of a small quantum system. The nonclassicality of the photon statistics leads to the possibility of switching between the phases.