Probing the thermodynamic limit of the photon blockade breakdown phase transition

The photon blockade breakdown process (PBB) in the driven-dissipative Jaynes-Cummings model has been identified as an example for a first order quantum phase transition. In this work, we experimentally study the PBB using one superconducting transmon qubit coupled to a single resonator mode in the presence of a strong resonant drive. We back out the phase diagram and the characteristic switching time scales as a function of drive detuning and normalized coupling strength g/κ with g being the qubit - photon coupling strength and κ the in-situ controlled cavity linewidth. For the smallest κ, we observe a mean switching timescale of up to 6 seconds, which is more than seven orders of magnitude longer than the characteristic lifetime of the system without the applied drive tone. This longtime stabilization of two macroscopic phases by a single qubit provides convincing evidence for the interpretation of the PBB as a first order quantum phase transition in a finite-size zero-dimensional system with a well-defined thermodynamic limit.