A high-resolution microchip optomechanical accelerometer

The monitoring of acceleration is essential for a variety of applications ranging from inertial navigation to consumer electronics1,2. Typical accelerometer operation involves the sensitive displacement measurement of a flexibly mounted test mass, which can be realized using capacitive3,4, piezoelectric5, tunnel-current6,7 or optical8–11 methods. Although optical detection provides superior displacement resolution8, resilience to electromagnetic interference and long-range readout7, current optical accelerometers either do not allow for chip-scale integration or utilize relatively bulky test mass sensors of low bandwidth8–10. Here, we demonstrate an optomechanical accelerometer that makes use of ultrasensitive displacement readout using a photonic-crystal nanocavity12 monolithically integrated with a nanotethered test mass of high mechanical Q-factor13. This device achieves an acceleration resolution of 10 mg Hz with submilliwatt optical power, bandwidth greater than 20 kHz and a dynamic range of greater than 40 dB. Moreover, the nanogram test masses used here allow for strong optomechanical backaction14–17, setting the stage for a new class of motional sensors. Owing to the rapid development of silicon micromachining technology, microelectromechanical systems (MEMS) accelerometers have become exceedingly popular over the past two decades1. Evolving from airbag deployment sensors in automobiles to tilt sensors in cameras and consumer electronics products, they can now be found in a large variety of technological applications with very diverse requirements for their performance metrics. For example, sensors for inertial navigation systems require low noise levels and superior bias stability18, but large bandwidth is crucial for sensors in acoustics and vibrometry applications19. However, there is a fundamental tradeoff between noise performance and bandwidth that can be understood from the basic principle of operation of an accelerometer (Fig. 1a). When subjected to an acceleration a(v) at frequency v, a mechanically compliant test mass experiences a displacement x(v)1⁄4 x(v)a(v) proportional to the mechanical susceptibility x(v)1⁄4 vm 2 vþ i[(vvm)/Qm]. Here, vm1⁄4 2pfm1⁄4 p (k/m) is the (angular) resonance frequency of the oscillator and Qm is its mechanical Q-factor (see the plot of |x(v)|1⁄4|x|/a in Fig. 1b for Qm1⁄4 10). Usually, accelerometers are operated below their fundamental resonance frequency vm , where x(v)≈ 1/vm exhibits an almost flat frequency response. This naturally leads to a tradeoff between resolution and bandwidth, because the large resonance frequency required for high-speed operation results in vanishingly small displacements. As a result, the performance of the displacement sensor constitutes a central figure of merit of an accelerometer. In a cavity optomechanical system, a mechanically compliant electromagnetic cavity is used to resonantly enhance the readout of mechanical motion20 (canonically, the motion of the end mirror of a Fabry–Perot cavity). Such systems have enabled motion detection measurements with an imprecision at or below the standard quantum limit (SQL)21, corresponding to the position uncertainty in the quantum ground state of the mechanical object. Furthermore, the average optical radiation pressure force can be quite large in microand nanoscale optomechanical devices, therefore offering the unique capability of controlling the sensor bandwidth via the optical spring effect16,17 and the effective temperature of the sensor by means of passive damping14 or feedback cold-damping15,22. In this Letter, we utilize an integrated SiN zipper photoniccrystal optomechanical cavity12 to provide shot-noise-limited readout of mechanical motion with imprecision near the SQL, enabling high-bandwidth and high-resolution acceleration sensing. The resolution of an accelerometer can be quantified by noise-equivalent acceleration, NEA1⁄4p(a th 2 þ adet 2 þ aadd 2 ), in units of g Hz (1 g1⁄4 9.81 m s). The first term in the NEA arises from thermal Brownian motion of the test mass (Supplementary Section SVI.a)23 and is given by