Time-of-flight force sensing below the quantum zero-point fluctuation

TL;DR

This paper demonstrates quantum-limited force sensing using a levitated nanoparticle below zero-point fluctuation by modulating trap stiffness and performing time-of-flight measurements.

Contribution

It introduces a method of rapid potential modulation to achieve force sensing below the quantum zero-point fluctuation in a levitated nanomechanical oscillator.

Findings

Achieved sensing of 10 zeptonewtons static force.

Performed quantum state tomography of the squeezed state.

Reconstructed the Wigner quasiprobability distribution.

Abstract

Sensing weak forces through observing a mechanical motion near or below its quantum zero-point fluctuation has been desired in diverse areas. While mechanical oscillators have played a crucial role in such studies, their application to free-fall-type sensing has been elusive, in particular in the quantum regime. Here, we demonstrate sensing a static force of the order of 10 zeptonewtons with a levitated nanomechanical oscillator below the zero-point fluctuation through the rapid modulation of its confining potential. We prepare a squeezed state with a reduced velocity uncertainty by abruptly decreasing the potential. Subsequently, we detect the exerted static force through time-of-flight measurements, where we release the nanoparticle from the potential and measure the displacement during a free fall. Furthermore, time-of-flight measurements allow us to perform quantum state tomography of the squeezed state, from which we reconstruct its Wigner quasiprobability distribution and evaluate the Fisher information for the position measurement to quantify the achievable force sensitivity of our protocol. Our results demonstrate that modulating the trap stiffness serves as a crucial technique for quantum-limited force sensing and paves the way to utilize a levitated nanoparticle as a promising sensing platform beyond the quantum limit with a capability of quantum state tomography.