Chirped nonlinear cavity for digital quantum state readout without switching

We observe a new phase-locking effect in a high-$Q$ cavity embedding a Josephson junction driven with a chirped microwave signal. Above a critical drive amplitude, the cavity phase-locks to the drive and its oscillation amplitude grows with time. Below threshold, the cavity dephases from the drive and its amplitude remains small. The transition to phase-locking is associated with a sharp threshold sensitive to the junction $I_0$, and can be used for digital detection of quantum states. This detector smoothly evolves into one oscillation state or the other without relying on any switching process.