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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum limit of the resolution in force measurement in an active interferometric optical displacement transducer

Andrey B. Matsko

Published May 6, 1996• 0 citations
Publisher

Abstract

The quantum limit for resolution in force measurement using active interferometric optical transducer of displacement is proved to be less than the standard quantum limit (SQL) if one measures not the phase but a specially chosen quadrature amplitude in the output wave, squeezed by a mechanism of ponderomotive nonlinearity. Consideration of two types of active transducer having three-level atoms gain and parametric gain is given. Noises of spontaneous emission, fluctuations due to losses in mirrors and effect of radiative friction are taken into account.

DOI
10.1117/12.239853

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The quantum limit for resolution in force measurement using active interferometric optical transducer of displacement is proved to be less than the standard quantum limit (SQL) if one measures not the phase but a specially chosen quadrature amplitude in the output wave, squeezed by a mechanism of ponderomotive nonlinearity. Consideration of two types of active transducer having three-level atoms gain and parametric gain is given. Noises of spontaneous emission, fluctuations due to losses in mirrors and effect of radiative friction are taken into account.
ABSTRACT The possibility of sensitivity improvement for parametric transducers with two-component pump by new algorithm of data processing is discussed. Keywords : Quantum noises , parametric systems , quantum non-demolation measurement , optimal filtration of vector signals 1. INTRODUCTION A measurement of a weak classical force acting on a high quality mechanical system plays an important role infundamental physical experiments with probe bodies (for example, in detection of cosmic gravitational waves). Anelaboration of a low noise sensitive element which is able to record a weak displacement of mechanical system is espessially essential in these experiments. The most perspective variant of such transducers is an optical Fabry-Perot interferometer in which one mirror is rigidly connected to a mass of a mechanical oscillator.A maximal sensitivity of a parametric transducer based on modulation of a reactive parameter of an electrical(optical) system is defined in non-regenerative regime by the standard quantum limit'
The interferometers now being developed to detect gravitational waves work by measuring the relative positions of widely separated masses. Two fundamental sources of quantum-mechanical noise determine the sensitivity of such an interferometer: (i) fluctuations in number of output photons (photon-counting error) and (ii) fluctuations in radiation pressure on the masses (radiation-pressure error). Because of the low power of available continuous-wave lasers, the sensitivity of currently planned interferometers will be limited by photon-counting error. This paper presents an analysis of the two types of quantum-mechanical noise, and it proposes a new technique---the "squeezed-state" technique---that allows one to decrease the photon-counting error while increasing the radiation-pressure error, or vice versa. The key requirement of the squeezed-state technique is that the state of the light entering the interferometer's normally unused input port must be not the vacuum, as in a standard interferometer, but rather a "squeezed state"---a state whose uncertainties in the two quadrature phases are unequal. Squeezed states can be generated by a variety of nonlinear optical processes, including degenerate parametric amplification.
The high-sensitivity quantum detection of a resonant classical force acting on a quantum harmonic oscillator can be significantly improved by employing a resonant optical parametric transducer. This technique leverages the unique properties of parametric interactions to enhance the response of the measurement system while maintaining quantum-limited performance. We demonstrate that such a configuration not only enables quantum back-action evading (BAE) measurements, surpassing the Standard Quantum Limit (SQL) of sensitivity, it also provides a mechanism for noiseless amplification of the classical signal. The key to this enhancement lies in the ability of the parametric transducer to generate and separately measure the upper and lower modulation sidebands induced by the external force. By decoupling and analyzing these sidebands independently, the system becomes capable of amplifying the signal without introducing additional noise, effectively circumventing quantum measurement constraints.