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.     

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.     

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.     

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.     

Reservoir Engineering Strong Magnomechanical Entanglement via Dual-Mode Cooling

A hybrid cavity magnomechanical system to transfer the bipartite entanglements and achieve the strong microwave photon–phonon entanglement based on the reservoir engineering approach is constructed. The magnon mode is coupled to the microwave cavity mode via magnetic dipole interaction and to the phonon mode via magnetostrictive force (optomechanical-like). It is shown that the initial magnon-phonon entanglement can be transferred to the photon-phonon subspace in the case of these two interactions cooperating. In the reservoir-engineering parameter regime, the initial entanglement is directionally transferred to the photon-phonon subsystem, so a strong bipartite entanglement in which the magnon mode acts as the cold reservoir to effectively cool the Bogoliubov mode delocalized over the cavity and the mechanical deformation mode is obtained. Moreover, dual-mode cooling is realized by engineering the dissipation of photon and phonon modes within the target mode, which allows entanglement to be further enhanced. The results indicate that the steady-state entanglement is robust against temperature. The dual-mode cooling reservoir engineering scheme can potentially be extended to other three-mode quantum systems.     

J-C模型和原子-腔光力学系统中的纠缠交换

基于Jaynes-Cummings模型和原子-腔光力学系统,研究了该系统中原子与机械模之间的纠缠交换机制,讨论了两个原子的相干角和腔场与机械模之间的耦合系数对原子与机械模之间纠缠的影响。一个原子与机械模之间的最大纠缠随着该原子相干角的增大而减小,另一个原子与机械模之间的纠缠存在突然产生和突然死亡现象,并且最大纠缠随该原子相干角的增大而增大。根据这一结果可以制备原子与机械模之间的最大纠缠态,这为纠缠调控提供了一种新的方式。     

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.     

Distributed entanglement in the two-photon two-mode non-linear process

In this paper we consider a quantum optics model where two-mode quantum light cavity with Kerr-like medium is coupled to an atom via two-photon process. The dynamical evolution of the system is studied in terms of entanglement measured by quantum relative entropy. The entanglements for the different bipartite partitions of the system, i.e., atom-two modes, mode-mode, mode-(atom+mode), are calculated explicitly and interesting trade-off relations between the different kinds of entanglement can be observed in different cases. The results show the entanglement between mode-mode is generally out of phase with that between atom and two modes, even though the two modes do not interact directly, and the Kerr-like medium prevents the atom and two modes from entangling.     

Optomechanical Entanglement Between an Ion and an Optical Cavity Field

I study an optomechanical system in which the mechanical motion of a single trapped ion is coupled to a cavity field for the realization of a strongly quantum correlated two-mode system. I show that for large pump intensities the steady state photon number exhibits bistable behaviour. I further analyze the occurrence of normal mode splitting (NMS) due to mixing of the fluctuations of the cavity field and the fluctuations of the ion motion which indicates a coherent energy exchange. I also find that in the parameter regime where NMS exists, the steady state of the system shows continuous variable entanglement. Such a two-mode optomechanical system can be used for the realization of continuous variable quantum information interfaces and networks.     

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 for a Bimodal Cavity Field Interacting with a Two-Level Atom

Negativity has been adopted to investigate the entanglement in a system composed of a two-level atom and a two-mode cavity field. Effects of Kerr-like medium and the number of photon inside the cavity on the entanglement are studied. Our results show that atomic initial state must be superposed, so that the two cavityfield modes can be entangled. Moreover, we also conclude that the number of photon in the two cavity mode should be equal. The interaction between modes, namely, the Kerr effect, has a significant negative contribution. Note that the atom frequency and the cavity frequency have an indistinguishable effect, so a corresponding approximation has been made in this article. These results may be useful for quantum information in optics systems.     

Effects of dipole-dipole interaction on entanglement transfer

A system consisting of two different atoms interacting with a two-mode vacuum, where each atom is resonant only with one cavity mode, is considered. The effects of dipole-dipole （dd） interaction between two atoms on the atom-atom entanglement and mode--mode entanglement are investigated. For a weak dd interaction, when the atoms are initially separable, the entanglement between them can be induced by the dd interaction, and the entanglement transfer between the atoms and the modes occurs efficiently; when the atoms are initially entangled, the entanglement transfer is almost not influenced by the dd interaction. However, for a strong dd interaction, it is difficult to transfer the entanglement from the atoms to the modes, but the atom-atom entanglement can be maintained when the atoms are initially entangled.     

Dynamics of entanglement transfer from radiation modes to localized qubits

We address the dynamics of entanglement transfer from two radiation modes to a pair of localized qubits implemented as atoms flying through or trapped in separated cavities. We first generalize previous results to include radiation in entangled mixed states and to describe the effect of cavity mirror transmittance. Then we investigate the transfer process by Monte Carlo Wave Function approach, which allows us to solve the whole system dynamics including cavity mode and atomic decays. We focus on flying modes prepared in coherently correlated states and we find realistic conditions for efficient entanglement transfer out of the weak and strong coupling regimes in the perspective of quantum memories realization.     

Feedback-controlled nonresonant laser cooling

We present a new approach to nonresonant laser deceleration and cooling of atoms based on their interaction with a bistable optical cavity. The cooling mechanism presents a photonic version of Sisyphus cooling, in which the conservative motion of atoms is interrupted by sudden transitions between two stable states of the cavity mode. The mechanical energy is extracted due to the hysteretic nature of those transitions. The bistable character of the cavity may be achieved by an external feedback loop, or by means of nonlinear intracavity optical elements. In contrast to the conventional cavity cooling, in which atoms experience a viscoustype force, bistable cavity cooling imitates “dry friction” and stops atoms much faster. Based on this novel approach, we explore the prospects of using optical bistability for efficient radiation pressure cooling of micromechanical devices that are modeled as a Fabry-Perot resonator with one fixed and one oscillating mirror. In all cases, analytical results are presented, supported by realistic numerical examples.     

Factors influencing entanglement of two excitons in a coupled exciton-photon system

The relation between the excitonic purity and the concurrence in a system of two coupled large semiconduction quantum dots mediated by a single-mode cavity field is investigated by using linear entropy theory. The results show the difference in describing two modes of excitonic entanglement between linear entropy and concurrence. The relation between nonclassical property of cavity field and the entanglement degree of excitons is also discussed. The results show that two modes of exciton can reach maximal entanglement when the cavity exhibits an antibunching effect.     

Continuous-Variable Entanglement Generation from a Four-State Atom under Raman Excitation

We investigate the generation and the evolution of continuous-variable (CV) entanglement from a laser-driven four-state atom inside a doubly resonant cavity under Raman excitation. Two transitions in the four-state atom independently interact with the two cavity modes, while two other transitions are driven by coupling laser fields. By including the atomic relaxation as well as cavity losses, we show that the CV entanglement with large mean number of
photons can be generated in our scheme. We also show that the intensity of the coupling laser fields can influence effectively the entanglement period of the cavity field. Different from the conventional resonant excitation scheme where zero one-photon detuning are required, it is found that the intensity and period of entanglement between the two cavity modes as well as the total mean photon number of the cavity field can be adjusted by properly
modulating the frequency detuning.     

Generalized Rotating-Wave Approximation for the Quantum Rabi Model with Optomechanical Interaction

The spectrum of energy and eigenstates of an hybrid cavity optomechanical system, where a cavity field mode interacts with a mechanical mode of a vibrating end mirror via radiation pressure and with a two level atom via electric dipole interaction are investigated. In the spirit of approximations developed for the quantum Rabi model beyond rotating-wave approximation (RWA), the so-called generalized RWA (GRWA) to diagonalize the tripartite Hamiltonian for arbitrary large couplings is implemented. Notably, the GRWA approach still allows to rewrite the hybrid Hamiltonian in a bipartite form, like a Rabi model with dressed atom-field states (polaritons) coupled to mechanical modes through reparametrized coupling strength and Rabi frequency. A more accurate energy spectrum for a wide range of values of the atom-photon and photon–phonon couplings, when compared to the RWA results is found. The fidelity between the numerical eigenstates and its approximated counterparts is also calculated. The degree of polariton-phonon entanglement of the eigenstates presents a non-monotonic behavior as the atom-photon coupling varies, in contrast to the characteristic monotonic increase in the RWA treatment.     

Entanglement transfer from two-mode squeezed vacuum light to spatially separated mechanical oscillators via dissipative optomechanical coupling

In this paper, we propose a scheme to generate an entangled state between two spatially separated movable mirrors by injecting the two-mode squeezed optical reservoir to the dissipative optomechanics, in which the movable mirrors can modulate the linewidth of the cavity modes. When the coupling between the mirrors and the corresponding cavity modes is weak, the two driven cavity fields can respectively behave as the squeezed-vacuum reservoir for the two movable mirrors by utilizing the effect of completely destructive interference of quantum noise. Thus the mechanical modes are prepared in a two-mode squeezed vacuum state. Moreover,when the coupling between the two mirrors and the cavities modes is strong, the entanglement between the two movable mirrors decreases because photonic excitation can preclude the completely destructive interference of quantum noise, but the movable mirrors are still entangled.     

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.     

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