Charge sensitivity of a cavity-embedded Cooper pair transistor limited by single-photon shot noise

Abstract

Using an 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 tunable, strongly nonlinear system affording a diverse range of functionalities, 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 of ≲1. Assuming realizable cCPT parameters [B. L. Brock et al., Phys. Rev. Applied 15, 044009 (2021)], and not including noise from the subsequent amplifier chain, we predict the fundamental, photon shot noise-limited charge sensitivity to be 0.12μe/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 a first reported charge sensitivity value of 14μe/Hz in the single-photon regime [B. L. Brock et al., arXiv:2102.05362 (2021)].

Feedback stabilization of the resonant frequency in tunable microwave cavities with single-photon occupancy

“…The magnitude of these resonant frequency fluctuations at some bias points is of the order of the cavity linewidth, shifting the carrier signal away from the cavity resonance during the course of a measurement. As a result, although the cCPT is capable of achieving quantum-limited electrometry at very low pump powers [27], the observed charge sensitivity is nearly three times worse than the theoretical predictions [9].…”

“…Following the formalism in Sec. II, we now have the bias vector b = (n g , Φ ext ) and the resonant frequency shift δω 0 ( b) inversely proportional to the Josephson inductance L CPT given by [26,27]…”

“…The cavity is driven using a carrier signal ω c = ω 0 (b 0 ) phase modulated with a modulation amplitude β and modulation frequency ω m several times larger than the cavity linewidth κ tot . As we are particularly interested in cases where the cavity is driven at very low pump powers, we will apply the formulation used in [27] to describe the resulting system dynamics via an operator scattering approach.…”