Preparation Of EPR-entangled Mechanical State

Rapid advancement of micro fabrication techniques including ground-state cooling,strong optomechanical coupling,optomechanically induced transparency in cavity optomechanics promotes the control and measurement of massive mechanical oscillators as well as further applications in ultrahigh-precision sensing and quantum information processing.Of particular fundamental interest is to investigate the entanglement in macroscopicscale,which is critical for a deeper understanding of the boundary between the classical and quantum world.Therefore,the possibility of entangling twomechanical oscillators has been widely investigated,such a sexploring the ponderomotive force,injecting entangled fields,modulating the optomechanical coupling,etc.In particular,continuous-variable(CV)Einstein–Podolsky–Rosen(EPR)entanglement represents a figure of merit for characterizing the efficacy of entanglement-based CV quantum information protocols,including quantum key distribution,quantum teleportation,and entanglement swapping.Therefore,this thesis is devoted to the investigation of preparation of the EPR entangled mechanical state in cavity optomechanics.EPR entanglement states are achievable by combining two single-mode position and momentum squeezed states at a 50:50 beam splitter(BS).The method is adoptable to prepare the EPR entangled mechanical state by linearly mixing two single-mode position and momentum squeezed mechanical states.Therefore,avariety of schemes of generating mechanical squeezing emerge which can extend to mechanical EPR entanglement such as reservoir engineering,inputting squeezed field on the cavity and employing parametric optomechanical resonator which is formed by a optical parametric amplifier(OPA)inside the optomechanical cavity.Moreover,entanglement of macroscopic oscillators is fragile to the unavoidable decoherence and dissipation caused by the surrounding thermal noise.Luckily,besides squeezing the mechanical motion,squeezed light and OPA can help to more efficiently cool the motion of a macroscopic mechanical object below the quantum limit to suppress the influence of thermal noise on the mechanical state,and also increase the optomechanical interaction even into the single-photon strong-coupling regime,which provides the possibility to achieve the mechanical entanglement under a relatively high temperature.We propose a scheme for the generation of EPR entangled mechanical state in a system consisted of two parametric optomechanical resonators,where a degenerate OPA is placed inside each cavity,and two mechanical oscillators are linearly coupled via either Coulomb.The linear coupling leads to the symmetric and antisymmetric combinations of two mechanical modes,which corresponds to a 50:50 BS mixing.In the linearized and weak optomechanical coupling regime,the cavity field serves as a squeezed environment due to the parametric interaction of cavity mode,and the squeezing can be transferred to the symmetricand antisymmetric mechanical modes.By choosing the opposite phases of parametric interactions,the position and momentum squeezing of mechanical modes are obtained.Then with the assistance of 50:50 BS-like mixing,EPR entangled mechanical state is achieved.In addition,the cavity-assisted cooling is enhanced by the parametric interactions,and the influence of the mechanical thermal noise on the entanglement can be significantly suppressed.We also investigate the generation of the EPR entangled state of two vibrating membranes in a ring resonator,where clockwise(CW)and counter-clockwise(CCW)travelling-wave modes are driven by lasers and finite-bandwidth squeezed lights.Since the optomechanical coupling depends on the location of the membranes,CW and CCW can couple to the symmetric and antisymmetric combination of mechanical modes for a suitable arrangement,which corresponds to a 50:50 BS mixing.Moreover,by employing the red-detuned driving laser and tuning the central frequency of squeezing field blue detuned from the driving laser with a mechanical frequency,the squeezing property of squeezed light can be perfectly transferred to the mechanical motion in the weak coupling regime.Thus,the BS mixing modes can be position and momentum squeezed by feeding the appropriate squeezed lights respectively,and the EPR entangled mechanical state is obtained.Moreover,cavity-induced mechanical cooling can further suppress the influence of thermal noise on the entangled state.The thesis is organized is as follows.In Section 1,we introduce the relevant basic knowledge used in the following.In Section 2,we propose a scheme for the generation of EPR entangled mechanical state in a system consisted of two parametric optomechanical resonators.In section 3,We propose scheme for the generation of the EPR entangled state of two vibrating membranes in a ring resonator.In section 4,the conclusion for our research content is drawn.