Charge sensitivity of a cavity-embedded Cooper pair transistor in the single-photon quantum noise limit.

Using a field operator scattering approach, we analyze the quantum dynamics of an ultrasensitive electrometer - a Cooper pair transistor embedded in a quarter-wave microwave cavity (cCPT). While the cCPT is inherently a strongly nonlinear system, we restrict our present analysis to a necessary first investigation of its linear charge sensing capabilities, limiting to low pump powers corresponding to an average cavity photon number $\lesssim 1$. Assuming realizable cCPT parameters similar to those obtained from a characterization of an actual experimental device (B. L. Brock et al., arXiv:2011.06298), we predict the fundamental, quantum noise-limited charge sensitivity to be $0.12\, \mu{\mathrm{e}}/\sqrt{\mathrm{Hz}}$ when the pumped cavity has an average of one photon and the cCPT is operated close to charge degeneracy. This is to be compared with our first reported charge sensitivity value $14\, \mu{\mathrm{e}}/\sqrt{\mathrm{Hz}}$ in the single-photon regime (B. L. Brock {\it et al}., arXiv:2102.05362)