Research On The Entanglement Of Orbital Angular Momentum In A Quantum Optomechanical System

The fundamental mechanism that couples the cavity radiation field to the mechanical motion is the momentum transfer of photons.In addition to linear momentum,photons may also carry angular momentum.The spin angular momentum which is labeled as the polarization of light has been fully described.However,the orbital angular momentum that results from the helical phase structure could extend the applications of quantum mechanics to an unprecedented degree.Recently experiments have demonstrated that the photon pairs generated in spontaneous parametric down-conversion(SPDC)are entangled in orbital angular momentum(OAM).Radiation pressure plays an important role in generating entanglement.It has previously been shown theoretically that radiation pressure can entangle a light field to a vibrating mirror in a cavity and hence the mirror to mirror in a double-vibrating-mirror-cavity system.But in those proposals most of cavity optomechanics has addressed vibrational motion hence the exchange of linear momentum between the photons.This paper will pay attention to the rotational motion corresponding to the exchange of OAM.In this article we propose a scheme to realize the entanglement between two spatially distant mechanical rotors.We get OAM entangled photons generated through a SPDC process.Then the entangled photon pairs respectively enter in two remote and independent optomechanical cavities.Our purpose is to distribute the quantum correlations from the photons to the noninteracting mechanical modes of the cavities by exchange OAM.Lastly,we discuss the mirror-mirror entanglement may be effected by radiation detuning,the modulus of the squeezing parameter,orbital angular momentum carried by the cavity mode,total optical orbital angular momentum,and in-put optical modes.