Feedback Stabilization of the Resonant Frequency in a Tunable Microwave Cavity with Single-Photon Occupancy

We successfully demonstrate low-frequency noise suppression in the resonant-frequency fluctuations of a cavity-embedded Cooper-pair transistor (cCPT) driven at single-photon occupancy. In particular, we report a reduction in the resonant-frequency fluctuations caused by the internal charge noise over a bandwidth of approximately $1.4\phantom{\rule{0.2em}{0ex}}\text{kHz}$ when the cavity is driven at an average photon number $n=10$ and a bandwidth of 11 Hz for an average $n=1$. The gate-dependent tunability of the cCPT allows us to implement a feedback scheme derived from the Pound-Drever-Hall locking technique. This reduces fluctuations due to intrinsic charge noise, which otherwise interfere with the operation of the cCPT as a near quantum-limited electrometer. Our technique can be generalized to achieve frequency stabilization in tunable microwave resonators that play a vital role in today's quantum computing architectures, thereby moderating the limitations in detection caused by the intrinsic $1/f$ noise on such circuit devices. The work discusses the various aspects relating to the operation of a fully functional feedback loop down to the single-photon level.