Membrane-Based Optomechanical Accelerometry

Optomechanical accelerometers promise quantum-limited readout, high detection bandwidth, self-calibration, and radiation-pressure stabilization. We present a simple, scalable platform that enables these benefits with nano-g sensitivity at acoustic frequencies, based on a pair of vertically integrated Si3N4 membranes with different stiffnesses, forming an optical cavity. As a demonstration, we integrate an ultrahigh-Q (>107), millimeter-scale Si3N4 trampoline membrane above an unpatterned membrane on the same Si chip, forming a finesse F≈2 cavity. Using direct photodetection in transmission, we resolve the relative displacement of the membranes with a shot-noise-limited imprecision of 7fm/Hz, yielding a thermal-noise-limited acceleration sensitivity of 0.6μg/Hz over a 1-kHz bandwidth centered on the fundamental trampoline resonance (40 kHz). To illustrate the advantage of radiation-pressure stabilization, we cold damp the trampoline to an effective temperature of 4 mK and leverage the reduced energy variance to resolve an applied stochastic acceleration of 50ng/Hz in an integration time of minutes. In the future, we envision a small-scale array of these devices operating in a cryostat to search for fundamental weak forces such as dark matter.