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By adjusting the frequency of the cavity, we perform a microwave reflection measurement and directly probe the coherence and interference effects in a phase-sensitive Josephson parametric amplifier. We demonstrate the shift in the peak and the dip in the reflection spectra of the amplifier, which operates in the phase-sensitive mode. The behavior of the shift can be precisely controlled by tuning the pump power, the frequency of the cavity, and the relative phase between the incident signal and pump field. Theoretical simulations are in good agreement with the experimental results. These results provide an alternative way of controlling the parametric process by adjusting the frequency of the cavity.

We fabricate a microscale electromechanical system, in which a suspended superconducting membrane, treated as a mechanical oscillator, capacitively couples to a superconducting microwave resonator. As the microwave driving power increases, nonmonotonic dependence of the resonance frequency of the mechanical oscillator on the driving power has been observed. We also demonstrate the optical switching of the resonance frequency of the mechanical oscillator. Theoretical models for qualitative understanding of our experimental observations are presented. Our experiment may pave the way for the application of a mechanical oscillator with its resonance frequency controlled by the electromagnetic and/or optical fields, such as a microwave-optical interface and a controllable element in a superqubit-mechanical oscillator hybrid system.