  The photon blockade breakdown in a continuously driven cavity QED system has
been proposed as a prime example for a first-order driven-dissipative quantum
phase transition. But the predicted scaling from a microscopic system -
dominated by quantum fluctuations - to a macroscopic one - characterized by
stable phases - and the associated exponents and phase diagram have not been
observed so far. In this work we couple a single transmon qubit with a fixed
coupling strength $g$ to an in-situ bandwidth $\kappa$ tuneable superconducting
cavity to controllably approach this thermodynamic limit. Even though the
system remains microscopic, we observe its behavior to become more and more
macroscopic as a function of $g/\kappa$. For the highest realized $g/\kappa
\approx 287$ the system switches with a characteristic dwell time as high as 6
seconds between a bright coherent state with $\approx 8 \times 10^3$
intra-cavity photons and the vacuum state with equal probability. This exceeds
the microscopic time scales by six orders of magnitude and approaches the near
perfect hysteresis expected between two macroscopic attractors in the
thermodynamic limit. These findings and interpretation are qualitatively
supported by semi-classical theory and large-scale Quantum-Jump Monte Carlo
simulations. Besides shedding more light on driven-dissipative physics in the
limit of strong light-matter coupling, this system might also find applications
in quantum sensing and metrology.
