Nonstationary force sensing under dissipative mechanical quantum squeezing

TL;DR

This paper develops a theoretical framework for force sensing using dissipative mechanical quantum squeezing, demonstrating how nonstationary protocols can surpass stationary measurement limits by reducing thermal noise effects.

Contribution

It introduces a nonstationary measurement protocol that enhances force sensitivity beyond stationary limits through dissipative state preparation and optimized measurement schemes.

Findings

Imprecision and back-action noise can be suppressed by input field amplitudes.

Force noise spectral density cannot go below thermal fluctuations in stationary measurements.

Nonstationary protocols significantly improve force measurement sensitivity.

Abstract

We study the stationary and nonstationary measurement of a classical force driving a mechanical oscillator coupled to an electromagnetic cavity under two-tone driving. For this purpose, we develop a theoretical framework based on the signal-to-noise ratio to quantify the sensitivity of linear spectral measurements. Then, we consider stationary force sensing and study the necessary conditions to minimise the added force noise. We find that imprecision noise and back-action noise can be arbitrarily suppressed by manipulating the amplitudes of the input coherent fields, however, the force noise power spectral density cannot be reduced below the level of thermal fluctuations. Therefore, we consider a nonstationary protocol that involves non-thermal dissipative state preparation followed by a finite time measurement, which allows one to perform measurements with a signal-to-noise much greater than the maximum possible in a stationary measurement scenario. We analyse two different measurement schemes in the nonstationary transient regime, a back-action evading measurement, which implies modifying the drive asymmetry configuration upon arrival of the force, and a nonstationary measurement that leaves the drive asymmetry configuration unchanged. Conditions for optimal force noise sensitivity are determined, and the corresponding force noise power spectral densities are calculated.