Nonlinear Charge- and Flux-Tunable Cavity Derived From an Embedded Cooper-Pair Transistor

We introduce the cavity-embedded Cooper-pair transistor (cCPT), a device that behaves as a highly nonlinear microwave cavity whose resonant frequency can be tuned both by charging a gate capacitor and by threading flux through a superconducting loop. We characterize this device and find excellent agreement between theory and experiment. A key difficulty in this characterization is the presence of frequency fluctuations comparable in scale to the cavity linewidth, which deform our measured resonance circles in accordance with recent theoretical predictions [Brock et al., Phys. Rev. Appl. 14, 054026 (2020)]. By measuring the power spectral density of these frequency fluctuations at carefully chosen points in parameter space, we find that they are primarily a result of the $1/f$ charge and flux noise common in solid-state devices. Notably, we also observe key signatures of frequency fluctuations induced by quantum fluctuations in the cavity field via the Kerr nonlinearity.