Method and apparatus to implement frequency stabilization of a resonator

A method of characterizing frequency fluctuations of a resonator having a resonant frequency f0 utilizing a frequency fluctuation characterization apparatus, comprising the steps of:

• a) generating simultaneously, with at least one signal generator, two periodical driving signals having respective frequencies f1, f2, said frequencies being different from each other, but contained within a resonance linewidth of the resonator, generating a resonator drive signal responsive to the two periodical driving signals, and driving the resonator with the resonator drive signal;
• b) performing simultaneous measurements of a response signal of said resonator at the frequencies f1, f2, of said periodical driving signals, comprising measurements of time-varying phases of the response signal, with a signal sensing device;
• and
• c) computing a correlation between said measurements with a signal processor responsive to the signal sensing device, said correlation being indicative of frequency fluctuations of the resonator, said correlation being utilized in a feedback system to control a resonant frequency of the resonator to compensate for the frequency fluctuations.