Navigation, bio-tracking devices and gravity gradiometry are amongst the diverse range of applications requiring ultrasensitive measurements of acceleration. We describe an accelerometer that exploits the dispersive and dissipative coupling of the motion of an optical whispering gallery mode (WGM) resonator to a waveguide. A silica microsphere-cantilever is used as both the optical cavity and inertial test-mass. Deflections of the cantilever in response to acceleration alter the evanescent coupling between the microsphere and the waveguide, in turn causing a measurable frequency shift and broadening of the WGM resonance. The theory of this optomechanical response is outlined. By extracting the dispersive and dissipative optomechanical rates from data we find good agreement between our model and sensor response. A noise density of 4.5 µg·Hz − 1 2 with a bias instability of 31.8 µg (g = 9.81 m·s −2 ) is measured, limited by classical noise larger than the test-mass thermal motion. Closedloop feedback is demonstrated to reduce the bias instability and long term drift. Currently this sensor outperforms both commercial accelerometers used for navigation and those in ballistocardiology for monitoring blood flowing into the heart. Further optimization would enable short-range gravitational force detection with operation beyond the lab for terrestrial or space gradiometry.
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Abstract:We demonstrate simultaneous center-of-mass cooling of two coupled oscillators, consisting of a microsphere-cantilever and a tapered optical fiber. Excitation of a whispering gallery mode (WGM) of the microsphere, via the evanescent field of the taper, provides a transduction signal that continuously monitors the relative motion between these two microgram objects with a sensitivity of 3 pm. The cavity enhanced optical dipole force is used to provide feedback damping on the motion of the micron-diameter taper, whereas a piezo stack is used to damp the motion of the much larger (up to 180 µm in diameter), heavier (up to 1.5 × 10 −7 kg) and stiffer microsphere-cantilever. In each feedback scheme multiple mechanical modes of each oscillator can be cooled, and mode temperatures below 10 K are reached for the dominant mode, consistent with limits determined by the measurement noise of our system. This represents stabilization on the picometer level and is the first demonstration of using WGM resonances to cool the mechanical modes of both the WGM resonator and its coupling waveguide.
Following the first demonstration of a levitated nanosphere cooled to the quantum ground state in 2020 (U. Delić, et al. Science, vol. 367, p. 892, 2020), macroscopic quantum sensors are seemingly on the horizon. The nanosphere’s large mass as compared to other quantum systems enhances the susceptibility of the nanoparticle to gravitational and inertial forces. In this viewpoint, we describe the features of experiments with optically levitated nanoparticles (J. Millen, T. S. Monteiro, R. Pettit, and A. N. Vamivakas, “Optomechanics with levitated particles,” Rep. Prog. Phys., vol. 83, 2020, Art no. 026401) and their proposed utility for acceleration sensing. Unique to the levitated nanoparticle platform is the ability to implement not only quantum noise limited transduction, predicted by quantum metrology to reach sensitivities on the order of 10−15 ms−2 (S. Qvarfort, A. Serafini, P. F. Barker, and S. Bose, “Gravimetry through non-linear optomechanics,” Nat. Commun., vol. 9, 2018, Art no. 3690) but also long-lived quantum spatial superpositions for enhanced gravimetry. This follows a global trend in developing sensors, such as cold-atom interferometers, that exploit superposition or entanglement. Thanks to significant commercial development of these existing quantum technologies, we discuss the feasibility of translating levitated nanoparticle research into applications.
An accelerometer utilising the optomechanical coupling between an optical whispering gallery mode (WGM) resonance and the motion of the WGM cavity itself was prototyped and field-tested on a vehicle. We describe the assembly of this portable, battery operated sensor and the field-programmable gate array automation. Pre-trial testing using an electrodynamic shaker demonstrated linear scale-factors with <0.3% standard deviation (±6 g range where g = 9.81 ms−2), and a strong normalised cross-correlation coefficient (NCCC) of rICP/WGM=0.997 when compared with an integrated circuit piezoelectric (ICP) accelerometer. A noise density of 40 μg Hz−1/2 was obtained for frequencies of 2–7 kHz, increasing to 130 μg Hz−1/2 at 200 Hz, and 250 μg Hz−1/2 at 100 Hz. A reduction in the cross-correlation was found during the trial, rICP/WGM = 0.36, which we attribute to thermal fluctuations, mounting differences, and the noisy vehicle environment. The deployment of this hand-fabricated sensor, shown to operate and survive during ±60 g shocks, demonstrates important steps towards the development of a chip-scale device.
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