Noise characterization and frequency locking of superconducting flux-tunable resonators

Abstract

Superconducting flux-tunable resonators (FTRs) have recently gained interest in the field of quantum sensing due to their high magnetic flux sensitivity coupled with an efficient microwave readout mechanism. However, the performance of a flux-tunable resonator as a flux sensor is limited by its susceptibility to noise. Studying the broadband noise characteristics of such systems is therefore important for establishing the sensitivity limitations of the device and for developing feedback stabilization techniques. The goal of this thesis is to characterize the noise in superconducting resonators and to stabilize their frequency fluctuations using a feedback loop. A homodyne measurement scheme is used to read out the phase and amplitude quadrature noise characteristics of the resonators. To establish a proof of concept, the noise of a non-tunable coplanar waveguide resonator is first experimentally characterized and studied for different input powers. The existence of two-level-system (TLS)-induced noise is experimentally verified in the frequency band of 100 Hz–4 kHz, with an approximate spectral frequency dependence of 1/ √ f. The noise characteristics of the FTR are then studied for different flux responsivities, with the dominant flux noise found to lie in the frequency range of 10 Hz to 300 kHz and exhibiting a spectral frequency dependence of 1/f. A Pound–Drever–Hall (PDH) experimental setup is designed to stabilize the resonators. The characteristic PDH error signal for the non-tunable resonator is successfully generated and studied for different bandwidths. The PDH loop is modified to use the tunability of the FTR as a feedback mechanism. The unique challenges associated with the broader linewidth of the FTR are studied, and the limitations of the current experimental setup for feedback stabilization are identified. To account for limitations imposed by the input power, the dependence of the signal-to-noise ratio (SNR) on the intracavity photon number nc of the resonators is investigated. For the non-tunable resonator, the lowest resolvable signal is limited to ⟨nc⟩ ≈ 1000.