We show how stationary entanglement between an optical cavity field mode and a macroscopic vibrating mirror can be generated by means of radiation pressure. We also show how the generated optomechanical entanglement can be quantified, and we suggest an experimental readout scheme to fully characterize the entangled state. Surprisingly, such optomechanical entanglement is shown to persist for environment temperatures above 20 K using state-of-the-art experimental parameters.

It is shown that radiation pressure can be profitably used to entangle macroscopic oscillators like movable mirrors, using present technology. We prove a new sufficient criterion for entanglement and show that the achievable entanglement is robust against thermal noise. Its signature can be revealed using common optomechanical readout apparatus.

We provide a general framework to describe cooling of a micromechanical oscillator to its quantum ground state by means of radiation-pressure coupling with a driven optical cavity. We apply it to two experimentally realized schemes, back-action cooling via a detuned cavity and cold-damping quantum-feedback cooling, and we determine the ultimate quantum limits of both schemes for the full parameter range of a stable cavity. While both allow to reach the oscillator's quantum ground state, we find that back-action cooling is more efficient in the good cavity limit, i.e. when the cavity bandwidth is smaller than the mechanical frequency, while cold damping is more suitable for the bad cavity limit. The results of previous treatments are recovered as limiting cases of specific parameter regimes.

By using a generalization of the optical tomography technique we describe the dynamics of a quantum system in terms of equations for a purely classical probability distribution which contains complete information about the system.Comment: 12 pages, LATEX,preprint of Camerino University, to appear in Phys.Lett.A (1996

We propose a simple optomechanical model in which a mechanical oscillator quadrature could be "cooled" well below its equilibrium temperature by applying a suitable feedback to drive the orthogonal quadrature by means of the homodyne current of the radiation field used to probe its position. PACS numbers(s): 03.65. Bz, 42.50.Dv, 42.50.Vk The problem of considering a macroscopic oscillator in terms of Quantum Mechanics is usually avoided because one can obtain the right results without using any quantum mechanical hypothesys. When, however, one whishes to use it as a device to detect extremely small displacements due to very weak forces, as in the gravitational wave detectors, one has to be careful in considering it as a mere macroscopic object. Should one consider a macroscopic oscillator as a quantum oscillator, once all other possible noise sources were eliminated by using filters, screens, insulators etc., the ultimate criterion one has to satisfy is the one associated with the thermal noise [1,2]. For the harmonic oscillator it means k B T

Equations ͑22͒-͑28͒, which give the exact expressions for the stationary position and momentum variances of the mechanical oscillator in the detuning-induced back-action cooling case, contain a number of misprints. The correct expression of the two variances instead readsThe parameters s 1 and s 2 are, respectively, given by the stability conditions of Eqs. ͑20a͒ and ͑20b͒. At the ground state both variances are equal to 1 / 2 and therefore realizing ground state cooling means achieving b q , b p , d q , d p → 0. We also take the opportunity to comment on the definition of the feedback force of Eq. ͑39b͒ in terms of the estimated phase quadrature ␦Y est defined in Eq. ͑42͒. Dividing by ͱ in the definition of ␦Y est is customary in quantum feedback theory ͓1͔, and means assuming that the feedback action automatically compensates for the loss of signal due to nonideal detection, independently of the value of the feedback gain g cd . However, this choice may be misleading because the parameter g cd becomes the feedback gain without taking into account this automatic compensation and it is therefore dependent upon . A simpler choice which avoids this problem is to define ␦Y est without dividing by ͱ , i.e.,which is a sort of output phase quadrature integrated over the cavity bandwidth. In this way the parameter g cd coincides with the actual gain of the feedback loop. All the subsequent equations of the paper remain correct provided that one performs the rescaling g͑͒ → ͱ g͑͒, which implies g cd → ͱ g cd and g 2 → ͱ g 2 . This means in particular that the measurement noise term of Eq. ͑44͒ is independent of , while the feedback correction to the mechanical susceptibility in Eq. ͑45͒ becomes proportional to ͱ . In the limit → 0 therefore feedback is no longer able to modify the mechanical response and has the only effect of adding the measurement noise. ͓1͔ H. M. Wiseman and G. J. Milburn, Phys. Rev. Lett. 70, 548 ͑1993͒.PHYSICAL REVIEW A 79, 039903͑E͒ ͑2009͒

It is shown that because of the radiation pressure a Schrödinger cat state can be generated in a resonator with oscillating wall. The optomechanical control of quantum macroscopic coherence and its detection is taken into account introducing new cat states. The effects due to the environmental couplings with this nonlinear system are considered developing an operator perturbation procedure to solve the master equation for the field mode density operator. PACS number

We perform an analysis of the optomechanical entanglement between the experimentally detectable output field of an optical cavity and a vibrating cavity end-mirror. We show that by a proper choice of the readout (mainly by a proper choice of detection bandwidth) one can not only detect the already predicted intracavity entanglement but also optimize and increase it. This entanglement is explained as being generated by a scattering process owing to which strong quantum correlations between the mirror and the optical Stokes sideband are created. All-optical entanglement between scattered sidebands is also predicted and it is shown that the mechanical resonator and the two sideband modes form a fully tripartite-entangled system capable of providing practicable and robust solutions for continuous variable quantum communication protocols.