Optomechanical entanglement in a whispering-gallery cavity

The dynamics of the optomechanical entanglement between optical cavity field modes and a macroscopic mechanical breathing mode in a whispering-gallery cavity as well as the continuous variable entanglement between the phase-quadrature amplitudes of the two whispering-gallery modes have been analysed.Simulated results indicate that under state-of-the-art experimental conditions,optomechanical entanglement is obvious and can occur even at temperatures of above 40 K.Compared with the entanglement of the mechanical oscillator at the ground state temperature,optomechanical entanglement is more intense by several orders of magnitude.     

Entangling Cavity Modes in a Double-Cavity Optomechanical System

We study entanglement of the cavity modes in a double-cavity optomechanical system in strong-coupling regime. The system is consist of two optomechanical systems coupled by a single photon hopping between them. With the radiation pressure of the photon, entanglement of the cavity modes can be generated. The average concurrence of the cavity modes is at least twice larger than that of the mechanical modes. Moreover, when we change the ratio between coupling strength and resonant frequency of mechanical modes, the entanglement in cavity and mechanical modes are influenced differently.     

Optomechanical dynamics in detuned whispering-gallery modes cavity

The dynamics of a microresonator in detuned whispering-gallery modes (WGM) cavity opto-mechanical system are investigated by the quantum Langevin equation. A WGM cavity coupling to two parallel waveguides is devised to study the transmission and reflection of this system. In single mode WGM cavity, without optomechanical coupling, both the transmission and reflection of the cavity present a Lorentzian dip and peak. When the coupling between the cavity mode and mechanical mode is considered, the transmission and reflection of the optomechanical cavity show “W” and “M” shape mode splitting. Moreover, under the action of a controlling and a probe laser, the output field at the probe frequency presents electromagnetically induced transparency (EIT)-like spectrum in the system. We give the physical origin of EIT-like and the pump-probe response for the WGM shares all the features of the Λ system in atoms. Further, due to backscattering, the two traveling waves in WGM are coupled with a rate γ. The transmission and reflection of the optomechanical cavity display three modes splitting in the spectra with optomechanical coupling between the two cavity modes and the mechanical mode.     

Nonreciprocal coupling induced entanglement enhancement in a double-cavity optomechanical system

We investigate the quantum entanglement in a double-cavity optomechanical system consisting of an optomechanical cavity and an auxiliary cavity, where the optomechanical cavity mode couples with the mechanical mode via radiation-pressure interaction, and simultaneously couples with the auxiliary cavity mode via nonreciprocal coupling. We study the entanglement between the mechanical oscillator and the cavity modes when the two cavities are reciprocally or nonreciprocally coupled. The logarithmic negativity $E_{n}^{(1)}$ ($E_{n}^{(2)}$) is adopted to describe the entanglement degree between the mechanical mode and the optomechanical cavity mode (the auxiliary cavity mode). We find that both $E_{n}^{(1)}$ and $E_{n}^{(2)}$ have maximum values in the case of reciprocal coupling. By using nonreciprocal coupling, $E_{n}^{(1)}$ and $E_{n}^{(2)}$ can exceed those maximum values, and a wider detuning region where the entanglement exists can be obtained. Moreover, the entanglement robustness with respect to the environment temperature is also effectively enhanced.     

Bistability and Entanglement of a Two-Mode Cavity Optomechanical System

We investigate the bistable properties and the entanglement in a two-mode cavity optomechanical system. Our results show that the bistable regime in terms of pumping amplitude can be adjusted by tuning the detunning. Although the two modes of the cavity interact with the same mechanical mode, there is no entanglement between them, while the two modes entangle with the mechanical mode seperately.     

Entanglement of Coupled Optomechanical Systems Improved by Optical Parametric Amplifiers

A scheme to generate the stationary entanglement of two distant coupled optical cavities placed optical parametric amplifiers is proposed. We study how the optical parametric amplifiers can affect the entanglement behaviors of the movable mirrors and the cavity fields. With the existence of optical parametric amplifiers, we show that larger stationary entanglement of optical and mechanical modes can be obtained and the entanglement increases with the increasing parametric gain. Especially, the degree of entanglement between the two cavity fields is more pronouncedly enhanced. Moreover, for a fixed parametric gain, the entanglement of distant cavity optomechanical systems increases as the input laser power is increased.     

Generating large steady-state optomechanical entanglement by the action of Casimir force

In this paper,we study an optomechanical device consisting of a Fabry-P′erot cavity with two dielectric nanospheres trapped near the cavity mirrors by an external driving laser.In the condition where the distances between the nanospheres and cavity mirrors are small enough,the Casimir force helps the optomechanical coupling to induce a steady-state optomechanical entanglement of the mechanical and optical modes in a certain regime of parameters.We investigate in detail the dependence of the steadystate optomechanical entanglement on external control parameters of the system,i.e.,the effective detuning,the pump powers of the cavity,the cavity decay rate and the wavelength of the driving field.It is found that the large steady-state optomechanical entanglement,i.e.EN=5.76,can be generated with experimentally feasible parameters,i.e.the pump power P=18.2μW,the cavity decay rateκ=0.5 MHz and the wavelength of the laserλL=1064 nm,which should be checked by optical measurement.     

Entanglement of movable mirror and cavity field enhanced by an optical parametric amplifier

A scheme to generate entanglement in a cavity optomechanical system filled with an optical parametric amplifier is proposed. With the help of the optical parametric amplifier, the stationary macroscopic entanglement between the movable mirror and the cavity field can be notably enhanced, and the entanglement increases when the parametric gain increases.Moreover, for a given parametric gain, the degree of entanglement of the cavity optomechanical system increases with increasing input laser power.     

Entanglement concentration with strong projective measurement in an optomechanical system

In this work, we study an entanglement concentration scheme in a 3-mode optomechanical system. The scheme is based on phonon counting measurements, which can be performed through photon counting of an auxiliary cavity connected to the mechanical resonator. The amount of entanglement between the two cavity output modes is found to increase logarithmically with the number of detected phonons(photons). Such an entanglement concentration scheme is deterministic since, independently of the number of detected phonons(photons), the measurement always leads to an increase in output entanglement. Besides numerical simulations,we provide analytical results and physical insight for the improved entanglement and the concentration efficiency.     

Entanglement and Output Squeezing of Distant Optomechanical Systems Generated by Four-Level Atoms

International Journal of Theoretical Physics - A scheme is presented to generate entanglement of optical andmechanical modes in coupled cavity optomechanical system with two four-level atoms. Two...     

Stationary entanglement between macroscopic mechanical oscillators

We show that the optomechanical coupling between an optical cavity mode and two movable cavity mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology. Received 2 September 2002 / Received in final form 10 October 2002 Published online 7 January 2003     

Optomechanical entanglement between a movable mirror and a cavity field

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.     

Quantifying non-classical correlations under thermal effects in a double cavity optomechanical system

We investigate the generation of quantum correlations between mechanical modes and optical modes in an optomechanical system,using the rotating wave approximation.The system is composed of two Fabry-Perot cavities separated in space;each of the two cavities has a movable end-mirror.Our aim is the evaluation of entanglement between mechanical modes and optical modes,generated by correlations transfer from the squeezed light to the system,using Gaussian intrinsic entanglement as a witness of entanglement in continuous variables Gaussian states,and the quantification of the degree of mixedness of the Gaussian states using the purity.Then,we quantify nonclassical correlations between mechanical modes and optical modes even beyond entanglement by considering Gaussian geometric discord via the Hellinger distance.Indeed,entanglement,mixdness,and quantum discord are analyzed as a function of the parameters characterizing the system(thermal bath temperature,squeezing parameter,and optomechanical cooperativity).We find that,under thermal effect,when entanglement vanishes,purity and quantum discord remain nonzero.Remarkably,the Gaussian Hellinger discord is more robust than entanglement.The effects of the other parameters are discussed in detail.     

Using coherent feedback loop for high quantum state transfer in optomechanics

We investigate the coherent feedback loop scheme to improve the quantum correlations transfer from optical to mechanical degrees of freedom in a double cavity optomechanical system. We use the Duan criterion to determine the separability of the two-mode mechanical states. The logarithmic negativity is employed to quantify the amount of the entanglement between mechanical modes in steady and dynamical regimes. We show that the entanglement can be significantly enhanced by a coherent feedback using a suitable tuning of the reflectivity parameter of the beam splitter located in each cavity. We also show that this enhancement is influenced by the temperature, the light squeezing parameter and the gain of the parameter amplifier. The entanglement dynamics in presence of the coherent feedback loop is also analyzed.     

Enhancing stationary optomechanical entanglement with the Kerr medium

We theoretically investigate the stationary entanglement of a optomechanical system with an additional Kerr medium in the cavity. There are two kinds of interactions in the system, photon-mirror interaction and photon-photon interaction. The optomechanical entanglement created by the former interaction can be effectively controlled by the latter one. We find that the optomechanical entanglement is suppressed by Kerr interaction due to photon blockage. We also find that the Kerr interaction can create the stationary entanglement and induce the resonance of entanglement in the small detuning regime. These results show that the Kerr interaction is an effective control for the optomechanical system.     

Quantum properties of nonclassical states generated by an optomechanical system with catalytic quantum scissors

A scheme is proposed to investigate the non-classical states generated by a quantum scissors device (QSD) operating on the the cavity mode of an optomechanical system. When the catalytic QSD acts on the cavity mode of the optomechanical system, the resulting state contains only the vacuum, single-photon and two-photon states depending upon the coupling parameter of the optomechanical system as well as the transmission coefficients of beam splitters (BSs). Especially, the output state is just a class of multicomponent cat state truncations at time t=2π by choosing the appropriate value of coupling parameter. We discuss the success probability of such a state and the fidelity between the output state and input state via QSD. Then the linear entropy is used to investigate the entanglement between the two subsystems, finding that QSD operation can enhance their entanglement degree. Furthermore, we also derive the analytical expression of the Wigner function (WF) for the cavity mode via QSD and numerically analyze the WF distribution in phase space at time t=2π. These results show that the high non-classicality of output state can always be achieved by modulating the coupling parameter of the optomechanical system as well as the transmittance of BSs.     

Quantum coherence transfer between an optical cavity and mechanical resonators

This study highlights the theoretical investigation of quantum coherence in mechanical oscillators and its transfer between the cavity and mechanical modes of an optomechanical system comprising an optical cavity and two mechanical oscillators that,in this study, were simultaneously coupled to the optical cavity at different optomechanical coupling strengths. The quantum coherence transfer between the optical and mechanical modes is found to depend strongly on the relative magnitude of the two optomechanical couplings. The laser power, decay rates of the cavity and mechanical oscillators, environmental temperature, and frequency of the mechanical oscillator are observed to significantly influence the investigated quantum coherences. Moreover,quantum coherence generation in the optomechanical system is restricted by the system's stability condition, which helps sustain high and stable quantum coherence in the optomechanical system.     

Generation of Steady-State Entanglement in Quadratically Coupled Optomechanical System Assisted by Two-Level Atoms

We propose a scheme for the realization of a hybrid, strongly entangled system formed of an atomic ensemble surrounded by a quadratically coupled optomechanical cavity with a vibrating mirror. We firstly investigate the steady-state bipartite entanglement between the movable mirror and the cavity mode with the help of an atomic media. It shows that the introduction of the atomic medium can greatly improve the entanglement between the movable mirror and the cavity mode. Secondly, steady-state tripartite entanglement including the movable mirror, the cavity and atom media are investigated. We find the robust tripartite entanglement persists in the present system.     

Reservoir-engineered entanglement in an unresolved-sideband optomechanical system

We study theoretically the generation of strong entanglement of two mechanical oscillators in an unresolved-sideband optomechanical cavity, using a reservoir engineering approach. In our proposal, the effect of unwanted counter-rotating terms is suppressed via destructive quantum interference by the optical field of two auxiliary cavities. For arbitrary values of the optomechanical interaction, the entanglement is obtained numerically. In the weak-coupling regime, we derive an analytical expression for the entanglement of the two mechanical oscillators based on an effective master equation, and obtain the optimal parameters to achieve strong entanglement. Our analytical results are in accord with numerical simulations.     

Cavity-mediated stationary atom–mirror entanglement in the presence of photothermal effects

We study stationary entanglement properties of an optomechanical system containing an atomic ensemble. We focus onto the case of the movable mirror strongly coupled to the cavity field through both radiation pressure and photothermal force. Exploiting a quantum Langevin equation approach we investigate the bipartite entanglement properties of various bipartite subsystems as well as stationary tripartite entanglement of the system. We particularly study robustness of the atom–mirror entanglement against temperature. We show that, even though the photothermal force is a dissipative force, it can significantly improve the cavity mediated atom–mirror entanglement.