© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:quant-ph/9905040 · Journal of Optics B Quantum and Semiclassical Optics

Quantum statistical properties of the radiation field in a cavity with a movable mirror

Constantin Brif, A. Mann

Published Feb 1, 2000• 13 citations

Abstract

A quantum system composed of a cavity radiation field interacting with a movable mirror is considered and quantum statistical properties of the field are studied. Such a system can serve, in principle, as an idealized meter for detection of a weak classical force coupled to the mirror which is modelled by a quantum harmonic oscillator. It is shown that the standard quantum limit on the measurement of the mirror position arises naturally from the properties of the system during its dynamical evolution. However, the force detection sensitivity of the system falls short of the corresponding standard quantum limit. We also study the effect of the nonlinear interaction between the moving mirror and the radiation pressure on the quadrature fluctuations of the initially coherent cavity field.

DOI: 10.1088/1464-4266/2/1/309

Related papers

Force sensitivity of a cavityless optomechanical system

R. Fermani, Stefano Mancini, David Vitali +1 more

We study the possibility to reveal a weak coherent force acting on a movable mirror (probe) by coupling it to a radiation field (meter) in a cavityless configuration. We determine the sensitivity of such a model and we show that the use of entangled meter state greatly improves the ultimate detection limit. A comparison of the presented model with that involving optical cavity is also done.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 25, 2004•0 citations

Quantum limited force measurement in a cavityless optomechanical system

R. Fermani, Stefano Mancini, Paolo Tombesi

We study the possibility of revealing a weak coherent force by using a pendular mirror as a probe, and coupling this to a radiation field, which acts as the meter, in a cavityless configuration. We determine the sensitivity of such a scheme and show that the use of an entangled meter state greatly improves the ultimate detection limit. We also compare this scheme with that involving an optical cavity.

arXiv:quant-ph/0312166•Physical Review A•Oct 4, 2004•16 citations

Quantum phase-space analysis of the pendular cavity

M. K. Olsen, A. B. Melo, K. Dechoum +1 more

We perform a quantum-mechanical analysis of the pendular cavity, using the positive-$P$ representation, showing that the quantum state of the moving mirror, a macroscopic object, has noticeable effects on the dynamics. This system has previously been proposed as a candidate for the quantum-limited measurement of small displacements of the mirror due to radiation pressure, for the production of states with entanglement between the mirror and the field, and even for superposition states of the mirror. However, when we treat the oscillating mirror quantum mechanically, we find that it always oscillates, has no stationary steady state, and exhibits uncertainties in position and momentum which are typically larger than the mean values. This means that previous linearized fluctuation analyses which have been used to predict these highly quantum states are of limited use. We find that the achievable accuracy in measurement is far worse than the standard quantum limit due to thermal noise, which, for typical experimental parameters, is overwhelming even at $2\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$

arXiv:quant-ph/0409214•Physical Review A•Oct 21, 2004•10 citations

Beating quantum limits in an optomechanical sensor by cavity detuning

O. Arcizet, Tristan Briant, A. Heidmann +1 more

We study the quantum limits in an optomechanical sensor based on a detuned high-finesse cavity with a movable mirror. We show that the radiation pressure exerted on the mirror by the light in the detuned cavity induces a modification of the mirror dynamics and makes the mirror motion sensitive to the signal. This leads to an amplification of the signal by the mirror dynamics, and to an improvement of the sensor sensitivity beyond the standard quantum limit, up to an ultimate quantum limit only related to the mechanical dissipation of the mirror. This improvement is somewhat similar to the one predicted in detuned signal-recycled gravitational-wave interferometers, and makes a high-finesse cavity a model system to test these quantum effects.

arXiv:quant-ph/0602040•Physical Review A•Mar 27, 2006•90 citations

Quantum-noise reduction using a cavity with a movable mirror

Claude Fabre, M. Pinard, S. Bourzeix +3 more

Because of radiation pressure, an optical cavity with harmonically bound mirrors has an intensity-dependent length and behaves as an effective Kerr medium. We determine the quantum fluctuations of the field reflected by such a cavity, taking into account the input field fluctuations and the mirror Brownian motion. In the regions of parameter space close to bistability turning points, we obtain a significant quantum-noise reduction effect.

Physical Review A•Feb 1, 1994•344 citations

Quantum optomechanical correlations induced by radiation pressure between light and mirrors

Tristan Briant, P. Verlot, Alexandros Tavernarakis +2 more

Radiation pressure exerted by light in interferometric measurements is responsible for displacements of mirrors which appear as an additional back-action noise and limit the sensitivity of the measurement. We experimentally study these effects by monitoring in a very high-finesse optical cavity the displacements of a mirror with a sensitivity at the 10-20m/√Hz level. This unique sensitivity is a step towards the first observation of the fundamental quantum effects of radiation pressure and the resulting standard quantum limit in interferometric measurements. Our experiment may become a powerful facility to test quantum noise reduction schemes, and we already have demonstrated radiation-pressure induced correlations between two optical beams sent into the same moving mirror cavity. Our scheme can be extended down to the quantum level and has applications both in high-sensitivity measurements and in quantum optics.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 29, 2008•2 citations

A quantum system composed of a cavity radiation field interacting with a movable mirror is considered and quantum statistical properties of the field are studied. Such a system can serve, in principle, as an idealized meter for detection of a weak classical force coupled to the mirror which is modelled by a quantum harmonic oscillator. It is shown that the standard quantum limit on the measurement of the mirror position arises naturally from the properties of the system during its dynamical evolution. However, the force detection sensitivity of the system falls short of the corresponding standard quantum limit. We also study the effect of the nonlinear interaction between the moving mirror and the radiation pressure on the quadrature fluctuations of the initially coherent cavity field.

We perform a quantum-mechanical analysis of the pendular cavity, using the positive-

P

representation, showing that the quantum state of the moving mirror, a macroscopic object, has noticeable effects on the dynamics. This system has previously been proposed as a candidate for the quantum-limited measurement of small displacements of the mirror due to radiation pressure, for the production of states with entanglement between the mirror and the field, and even for superposition states of the mirror. However, when we treat the oscillating mirror quantum mechanically, we find that it always oscillates, has no stationary steady state, and exhibits uncertainties in position and momentum which are typically larger than the mean values. This means that previous linearized fluctuation analyses which have been used to predict these highly quantum states are of limited use. We find that the achievable accuracy in measurement is far worse than the standard quantum limit due to thermal noise, which, for typical experimental parameters, is overwhelming even at

2\phantom{\rule{0.3em}{0ex}}\mathrm{mK}

We study the quantum limits in an optomechanical sensor based on a detuned high-finesse cavity with a movable mirror. We show that the radiation pressure exerted on the mirror by the light in the detuned cavity induces a modification of the mirror dynamics and makes the mirror motion sensitive to the signal. This leads to an amplification of the signal by the mirror dynamics, and to an improvement of the sensor sensitivity beyond the standard quantum limit, up to an ultimate quantum limit only related to the mechanical dissipation of the mirror. This improvement is somewhat similar to the one predicted in detuned signal-recycled gravitational-wave interferometers, and makes a high-finesse cavity a model system to test these quantum effects.

Radiation pressure exerted by light in interferometric measurements is responsible for displacements of mirrors which appear as an additional back-action noise and limit the sensitivity of the measurement. We experimentally study these effects by monitoring in a very high-finesse optical cavity the displacements of a mirror with a sensitivity at the 10-20m/√Hz level. This unique sensitivity is a step towards the first observation of the fundamental quantum effects of radiation pressure and the resulting standard quantum limit in interferometric measurements. Our experiment may become a powerful facility to test quantum noise reduction schemes, and we already have demonstrated radiation-pressure induced correlations between two optical beams sent into the same moving mirror cavity. Our scheme can be extended down to the quantum level and has applications both in high-sensitivity measurements and in quantum optics.