Abstract
We develop a stoichiometric silicon nitride (SiN) membrane-based electromechanical system, in which the spring constant of the mechanical resonator can be dynamically controlled via piezoelectric actuation. The degenerate parametric amplifier is studied in this configuration. We observe the splitting of mechanical mode in the response spectra of a phase-sensitive parametric amplifier. In addition, we demonstrate that the quality factor Q of the membrane oscillator can be significantly enhanced by more than two orders of magnitude due to the coherent amplification, reaching an effective Q factor of ∼3 × 108 at room temperature. The nonlinear effect on the parametric amplification is also investigated, as well as the thermomechanical noise squeezing. This system offers the possibility to integrate electrical, optical and mechanical degrees of freedom without compromising the exceptional material properties of SiN membranes, and can be a useful platform for studying cavity optoelectromechanics.
Highlights
Where x(t) is the membrane displacement, m is the effective mass, ω0 is the eigenfrequency of the mechanical oscillator, Q is the quality factor, k0 = mω[02] is the spring constant, kp(F0) is the amplitude of the pump (signal) field, ∆p(∆s) is the frequency detuning of the pump (signal) field, and φ denotes for the phase of the signal relative to the pump field
Silicon nitride (SiN) membranes have attracted a lot of interest due to their exceptional material properties, e.g. very high mechanical Q factors and ultralow optical absorption for near infrared light
The mechanical Q factors in most of these optoelectromechanical systems require to be further improved in order to obtain longer phonon lifetimes
Summary
Where x(t) is the membrane displacement, m is the effective mass, ω0 is the eigenfrequency of the mechanical oscillator, Q is the quality factor, k0 = mω[02] is the spring constant, kp(F0) is the amplitude of the pump (signal) field, ∆p(∆s) is the frequency detuning of the pump (signal) field, and φ denotes for the phase of the signal relative to the pump field. We consider the parametrically pumped mechanical response spectrum of the membrane oscillator under the degenerate case, where the pump frequency is always tuned to be twice the signal frequency, i.e.
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