The Quantum-Classical Correspondence for a Self-Oscillating Cavity-Embedded Cooper Pair Transistor System

We provide a theoretical model for our recent experiment involving a dc voltage biased Cooper pair transistor (CPT) that strongly drives a high quality factor microwave cavity via the ac Josephson effect. Depending on the tunable dc voltage bias, the model shows that the CPT can generate a range of non-trivial cavity quantum states involving large average microwave photon number. Using a Floquet basis approach to solving for the quantum dynamics and a Wigner function representation of the system state, we compare some of the model photon state predictions with experiment. The good agreement validates the low noise, dc biased cavity-CPT system for exploring the quantum-classical correspondence in strongly nonlinear, macroscopic systems.