Multi-Tone Microwave Locking via Real-Time Feedback

Abstract: Environmental noise coupling to mechanical experiments often introduces low-frequency fluctuations to the resonators, adding noise to measurements and reducing signal to noise. To counter these fluctuations, we demonstrate a dynamic feedback system implemented by the locking of a microwave drive to the noisy cavity. A homodyne interferometer scheme monitors the cavity resonance fluctuations due to low-frequency noise, which is mitigated by frequency-modulating (FM) the microwave generator. The feedback has a bandwidth of $400$ Hz, with a reduction of cavity fluctuations by $84\%$ integrating up to a bandwidth of $2$ kHz. Moreover, the cavity resonance frequency fluctuations are reduced by $73\%$. This scheme can be scaled to enable multi-tone experiments locked to the same feedback signal. As a demonstration, we apply the feedback to an optomechanical experiment and implement a cavity-locked, multi-tone mechanical measurement. As low-frequency cavity frequency noise can be a limiting factor in many experiments, the multi-tone microwave locking technique presented here is expected to be relevant for a wide range of fields of research.