Quantum noise in the mirror-field system: A field theoretic approach

TL;DR

This paper uses a field theoretic approach to analyze quantum noise in a mirror-field system, identifying sources of measurement uncertainty and conditions under which the standard quantum limit can be surpassed.

Contribution

It introduces a comprehensive field theoretic framework to study quantum noise, including correlations and backreaction effects, improving upon traditional particle number methods.

Findings

Quantum noise sources include shot noise, radiation pressure fluctuations, and field fluctuations.

Negative correlations can reduce measurement uncertainty below the standard quantum limit.

Backreaction effects are negligible for slow-moving mirrors.

Abstract

We employ the field theoretic approach to study the quantum noise problem in the mirror-field system, where a perfectly reflecting mirror is illuminated by a single-mode coherent state of the massless scalar field. The associated radiation pressure is described by a surface integral of the stress-tensor of the field. The read-out field is measured by a monople detector, form which the effective distance between the detector and mirror can be obtained. In the slow-motion limit of the mirror, we are able to identify various sources of quantum noise that lead to uncertainty of the read-out measurement. Since the mirror is driven by radiation pressure, the sources of noise, other than the shot nose given by the intrinsic fluctuations of the incident state, may also result from random motion of mirror due to radiation pressure fluctuations and from modified field fluctuations induced by the displacement of the mirror. Correlation between different sources of noise can be established as the consequence of interference between the incident field and the reflected field out of the mirror in the read-out measurement. The overall uncertainty is found to decrease (increase) due to the negative (positive) correlation. In the case of negative correlation, the uncertainty can be lowered than the value predicted by the standard quantum limit. We also examine the validity of the particle number approach, which is often used in quantum optics, and compared its results with those given by the field theoretical approach. Finally we discuss the backreaction effects, induced by the radiation pressure, that alter the dynamics of the mean displacement of the mirror, and we argue this backreaction can be ignored for a slowly moving mirror.