Strong actuation and optomechanical application of mass loaded membranes

Abstract

An increasing number of studies are moving towards the combination of quantum mechanics and gravity, where studying gravity from a very small source mass is a viable starting point. Preparing for such experiments, investigations of weak gravitational forces have employed mechanical resonators to detect time-dependent gravitational forces from actuated source masses. Here, we demonstrate a source mass approach which utilizes capacitive actuation of a 1 mg gold sphere embedded on a silicon nitride membrane, rather than piezoelectric or motorized actuation. The design simultaneously provides a method for microwave optomechanical implementation by coupling the membrane position to the electromagnetic mode of a 3D cavity. The cavity quality factor is not significantly compromised by electromagnetic leakage to the actuation electrode, allowing DC and kilohertz AC voltages to be introduced in the region where electric fields are strongly concentrated. We measure over 700 nm of driven oscillation amplitude and more than ten percent tunability in the mechanical resonance frequency of the loaded membrane, giving the potential to match the oscillations to the frequency range of a detector in future experiments. An optomechanical readout is demonstrated by measuring the cavity resonance at cryogenic temperatures, while room temperature measurements provide complimentary understanding of the mechanisms which influence the mechanical response, including repulsive contact due to collisions within the device.

Figures (7)

• Figure 1: Flipchip device schematic. (a) Equivalent circuit diagram used to simulate the voltage division within the system. (b) Side view and (c) top-down view of the device design. (d) Photograph of the device mounted in the 3D cavity sample holder.
• Figure 2: Simulating the electromagnetic mode inside the cavity using COMSOL. The antennas focus the electric field to produce a mode at 5.05 GHz, with a particularly large field strength in the center. The membrane metallization produces a mechanically compliant capacitor with the antennas to couple the cavity mode to the membrane displacement. The green box shows a variant of the antenna geometry which produces a large field at the membrane center while still having the gate electrode close by. The red box shows a less optimized design which perturbs the field at the center of the membrane, reducing the coupling strength.
• Figure 3: Tuning of the mechanical resonance frequency by applying a DC voltage between the membrane and gate electrode. The shift of frequency from its unbiased value is obtained by locating the mechanical resonance in the displacement spectrum, measured with a vibrometer. The black line is a theoretical fit determined by Eq. (\ref{['eq: omega_eff']}). Inset: An example of the measured displacement spectral density of the membrane (green), for the fundamental mechanical mode. The effective temperature of the mode is calculated by the area under the curve, with the black line showing the corresponding theoretical spectrum for this temperature, given by Eq. (\ref{['eq: FDT']}) after taking the background noise into account. The magenta line shows the background noise due to measurement imprecision, the red and blue lines show the thermal and vibrational contributions, respectively, to the displacement spectrum.
• Figure 4: Electrostatically actuated flipchip membrane (pictured in the inset). Each colored dataset shows the measured membrane oscillation amplitude when an AC drive is swept in frequency through the mechanical resonance in the positive direction, from 0.25 V (red) to 5 V (blue). At large amplitudes the response shows a strong hardening and discontinuous jumps due to a repulsive contact force between the membrane and chip below. The purple line shows the simulated response in the presence of a contact force for the largest drive.
• Figure 5: Inertial actuation of a membrane suspended from four support pillars, placed on a piezoelectric disc (pictured in the inset). Each colored dataset shows the measured membrane oscillation amplitude when an AC drive to the piezoelectric is swept in frequency through the mechanical resonance in the positive direction, from 0.2 V (red) to 4 V (blue). The response is characteristic of a Duffing oscillator, with the black line showing the fitted backbone given by Eq. (\ref{['eq: Duffing backbone']}).