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 sub-micro-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 ultra-high-Q (>10⁷), millimeter-scale Si₃N₄ trampoline (40 kHz fundamental resonance) above an unpatterned membrane (180 kHz) 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 7 fm/√Hz, yielding a thermal-noise-limited acceleration sensitivity of 600 nano-g/√Hz over a 1 kHz bandwidth centered on the trampoline resonance. We use radiation pressure to cold-damp the trampoline to an effective temperature of 4 mK and show that this method can be used to resolve stochastic accelerations as small as 50 ng/√Hz in integration times of minutes. In the future, we envision a F∼100 (using photonic crystal mirrors), centimeter-scale version of this device operating in a cryostat to search for fundamental weak forces such as vector dark matter.