Membrane-based Optomechanical Accelerometry

TL;DR

This paper introduces a scalable optomechanical accelerometer platform using Si3N4 membranes, achieving nano-g sensitivity at acoustic frequencies with quantum-limited readout and radiation pressure stabilization.

Contribution

The work demonstrates a simple, scalable membrane-based optomechanical accelerometer with ultra-high-Q membranes, achieving shot-noise-limited displacement detection and enhanced sensitivity through radiation pressure cooling.

Findings

Achieved 7 fm/√Hz displacement imprecision.

Realized 562 nG/√Hz acceleration sensitivity over 1 kHz bandwidth.

Successfully cold damped the membrane to 4 mK, resolving 50 nG/√Hz stochastic acceleration.

Abstract

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 Si$_3$N$_4$ membranes with different stiffnesses, forming an optical cavity. As a demonstration, we integrate an ultrahigh-Q ($>10^7$), millimeter-scale Si$_3$N$_4$ trampoline membrane above an unpatterned membrane on the same Si chip, forming a finesse $\mathcal{F}\approx2$ cavity. Using direct photodetection in transmission, we resolve the relative displacement of the membranes with a shot-noise-limited imprecision of 7 fm/$\sqrt{\text{Hz}}$, yielding a thermal-noise-limited acceleration sensitivity of 562 n$g/\sqrt{\text{Hz}}$ 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 50 n$g/\sqrt{\text{Hz}}$ 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.