Noise switching at a dynamical critical point in a cavity-conductor hybrid

Coupling a mesoscopic conductor to a microwave cavity can lead to fascinating feedback effects which generate strong correlations between the dynamics of photons and charges. We explore the connection between cavity dynamics and charge transport in a model system consisting of a voltage-biased Josephson junction embedded in a high-$Q$ cavity, focusing on the behavior as the system is tuned through a dynamical critical point. On one side of the critical point the noise is strongly suppressed, signaling the existence of a regime of highly coherent transport, but on the other side it switches abruptly to a much larger value. Using a semiclassical approach we show that this behavior arises because of the strongly nonlinear cavity drive generated by the Cooper pairs. We also uncover an equivalence between charge and photonic current noise in the system which opens up a route to detecting the critical behavior through straightforward microwave measurements.