A levitated nano-accelerometer sensitized by quantum quench

TL;DR

This work demonstrates a nanoscale inertial sensor based on a levitated nanoparticle near its quantum ground state, where a rapid quench of the trapping potential enhances acceleration sensitivity. By abruptly reducing the trap frequency, the system exhibits nonequilibrium dynamics that amplify the gravitational acceleration projection along the measurement axis, with an optimally timed readout governed by the minimum position uncertainty and a large displacement. The observed sensitivity is benchmarked against the quantum Fisher information bound and quantum Langevin simulations, showing good agreement and revealing background-gas heating as the dominant limitation. The results indicate a practical route to quantum-enhanced inertial sensing via quench dynamics, with potential improvements from lower background pressure and refined control of the optical setup to minimize spurious potential shifts.

Abstract

We realize a nanoscale accelerometer exploiting the nonequilibrium dynamics of a nanoparticle near the quantum ground state. We explore the dynamics after quenching the trapping potential and find that rapid quenching provides an instance at which the sensitivity is enhanced due to the minimized uncertainty in the position. With rapid quenching, the observed sensitivity is in good agreement with a numerical simulation based on the quantum Langevin equation and approaches to the limit given by the quantum Fisher information. Our results open up a pathway to quantum inertial sensing sensitized by exploiting quench dynamics.

Figures (7)

• Figure 1: Overview of the experiments.a, Schematic of our experimental setup. A nanoparticle is trapped in an optical lattice formed by a single-frequency laser. The light scattered by the nanoparticle is extracted through a Faraday isolator (FI) and is incident on a photodetector (PD). The signal from the PD is used for both feedback cooling and observing the motion along the optical lattice. The intensity of the laser is controlled by an acousto-optic modulator (AOM) driven by radio frequency (RF) from an arbitrary waveform generator (AWG). b, Time sequence of the each cycle of measurements. Feedback cooling of translational motions is turned off just before the quench. c, Mechanism of an accelerometer with quenching the potential. Due to the static acceleration, the minimum of the harmonic potential displaces with quenching the potential. The displacement induced by the quench $\mu$ is measured by recovering the initial laser intensity at the measurement time $T$. d, Variation of the uncertainties in the position ($z$) and the momentum ($p$) on the phase space during the quench dynamics. $z_0$ and $p_0$ denote the zero-point fluctuations in the position and the momentum, respectively.
• Figure 2: Quench dynamics due to the gravitational acceleration. Each symbol denotes data obtained under the following quench time constants: diamonds, $\tau_1 = { }1.95(2) ~ \mathrm{\mu s}$; triangles, $\tau_2 = { }3.77(3) ~ \mathrm{\mu s}$; circle, $\tau_3 = { }7.24(6) ~ \mathrm{\mu s}$; and square, $\tau_4 = { }14.9(1) ~ \mathrm{\mu s}$. The solid, dashed, dotted, and dot-dashed lines indicate numerical simulations based on the quantum Langevin equation for $\tau_1, \tau_2, \tau_3$, and $\tau_4$, respectively. a, Oscillatory dynamics of the distribution center $\mu$ after the quench. Each trace is vertically shifted by ${ }1 ~ \mathrm{nm}$. b, Time evolution of the distribution width $\sigma$ after the quench, exhibiting both coherent breathing-mode oscillations and monotonic increases due to environmental heating. Each trace is vertically shifted by ${ }0.05 ~ \mathrm{nm}$.
• Figure 3: Dependence of the quench dynamics on the table angle.a, Oscillations of $\mu$ for two tilt angles $\theta$ of ${ }0.25 ~ \mathrm{^\circ}$ (squares) and ${ }-0.31 ~ \mathrm{^\circ}$ (circles) under the shortest quench time of $\tau_1$. The solid lines show fits with Eq.(\ref{['eq:oscillation']}), from which the offset values shown in b, are extracted. b, The offset values obtained from fits as a function of the tilt angle $\theta$. The measurement is performed with the quench time constant of $\tau_1$. c, The difference between the two curves obtained from fits in a, as a function of $T$.
• Figure 4: Variation of the accelerometer sensitivity with the quench time. a, The maximum values of $S = (d\mu/da)/\sigma$ as a function of the quench time constant $\tau$. The solid line shows calculated values obtained numerical simulations without fitting parameters with a heating rate of ${ }16(2) ~ \mathrm{mK/s}$, which is obtained by minimizing the deviation in $\sigma$ between calculated and observed values. For comparison, simulated values for heating rates of ${ }6 ~ \mathrm{mK/s}$ and ${ }22 ~ \mathrm{mK/s}$, corresponding to two extreme cases that background gases consist of pure hydrogen or pure nitrogen, are also shown by red dashed and purple dotted lines, respectively. b, Allan deviation of the measured acceleration for three conditions: (1) $\tau_1$ at $T= { }89.7 ~ \mathrm{\mu s}$ (square), (2) $\tau_1$ at $T= { }46.3 ~ \mathrm{\mu}$s (circle), (3) $\tau_6 = { }72.9(5) ~ \mathrm{\mu s}$ at $T= { }540 ~ \mathrm{\mu s}$ (triangle). Maximizing the short-term sensitivity is crucial for achieving the high sensitivity for a long time.
• Figure 5: Time evolution of $\mu$ and $\sigma$ for slow quenching Each symbol denotes data obtained under the following quench time constants: squares, $\tau_5 = { }36.6(2) ~ \mathrm{\mu s}$; circles, $\tau_6 = { }72.9(3) ~ \mathrm{\mu s}$; The solid and dashed indicate numerical simulations for $\tau_5$ and $\tau_6$, respectively. The deviation in $\mu$ between experiments and calculations implies a potential drift that is not included in our simulation. a, Oscillatory dynamics of the distribution center $\mu$ after the quench. b, Time evolution of the distribution width $\sigma$ after the quench.