Generating EPR-entangled mechanical state via feeding finite-bandwidth squeezed light

Einstein–Podolski–Rosen(EPR) entanglement state is achievable by combining two single-mode position and momentum squeezed states at a 50:50 beam-splitter(BS). We 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.     

多个量子节点确定性纠缠的建立

量子纠缠是一种重要的量子资源,在多个空间分离的量子存储器间建立确定性的量子纠缠,然后在用户控制的时刻将所存储的量子纠缠转移到量子信道中进行信息的分发和传送,这对于实现量子信息网络是至关重要的.本文介绍了用光学参量放大器制备与铷原子D1吸收线对应的非经典光场,而且在三个空间分离的原子系综中确定性量子纠缠的产生、存储和转移.利用电磁感应透明光和原子相互作用的原理,将制备的多组分光场纠缠态模式映射到三个远距离的原子系综以建立原子自旋波之间的纠缠.然后,存储在原子系综中的纠缠态通过三个量子通道,纠缠态的量子噪声被转移到三束空间分离的正交纠缠光场.三束释放的光场间纠缠的存在验证了该系统具有保持多组分纠缠的能力.这个方案实现了三个量子节点间的纠缠,并且可以直接扩展到具有更多节点的量子网络,为未来实现大型量子网络通信奠定了基础.     

Transfer of quantum correlations in nonunitary evolution

A generalized Lindblad equation has been derived for describing the evolution of two dynamical systems interacting with a bath formed by two broadband modes of squeezed light in an entangled state. The transfer of quantum correlations, in particular, entanglement between the bath and dynamic systems, which are taken in the form of two electromagnetic field modes separated by two high-Q cavities, two atoms, and an atom and a mode, has been analyzed. It has been found that the entanglement of the bath is transferred both to two modes and to two atoms, which can form an almost perfect Einstein-Podolsky-Rosen pair. It has been shown that the interaction of the bath with the system consisting of an atom and a mode for which collective boson operators are introduced leads to the appearance of coherent and squeezed states.     

Entanglement swapping of continuous variable using squeezed vacuum states

We present a realistic scheme for the entanglement swapping of continuous variable, in which a two-mode squeezed vacuum state serves as a quantum channel. The position sum and momentum difference of two local modes are measured. By taking the input entangled state also as a two-mode squeezed vacuum state, we investigate the average fidelity and the von Neumann entropy of the output state. The results show that the perfect teleportation can be achieved by increasing the squeezing of the quantum channel and that any nonzero squeezing in both the quantum channel and the input entangled state is sufficient to swap the entanglement.     

Would one rather store squeezing or entanglement in continuous variable quantum memories?

Given two quantum memories for continuous variables and the possibility to perform passive optical operations on the optical modes before or after the storage, two possible scenarios arise resulting in generally different degrees of final entanglement. Namely, one could either store an entangled state and retrieve it directly from the memory, or rather store two separate single-mode squeezed states and then combine them with a beam-splitter to generate the final entangled state. In this Letter, we analytically determine which of the two options yields more entanglement for several regions of the system?s parameters, and quantify the advantage it entails.     

利用置于光腔中的非线性耦合器制备压缩和连续变量纠缠光

利用置于光腔中的非线性耦合器制备了压缩和连续变量纠缠光.通过特征函数方法解析求解了双模腔场满足的主方程.分析发现：在一定的条件下,此系统能产生稳定的双模压缩和连续变量纠缠光,且压缩和纠缠的强度与系统的耦合参量及腔场损耗系数密切相关.     

Preparation of entangled squeezed states and quantification of their entanglement

We propose a scheme for generating bipartite and multipartite entangled squeezed states via the Jaynes－Cummings model with large detuning. Bipartite entanglement of these entangled states is quantified by the concurrence. We also use the N-tangle to compute multipartite entanglement of these multipartite entangled squeezed states. Finally we discuss two limiting cases which arise from r→∞ and r→0, in which the multipartite entangled squeezed state reduces correspondingly into an N-qubit Greenberger－Horne－Zeilinger state and an N-qubit W state.     

纠缠微波信号的特性及表示方法

纠缠微波信号是电磁场微波频段量子特性的体现.在总结了现有纠缠微波信号产生及验证实验的基础上,针对目前没有统一的表达式来描述纠缠微波信号格式的问题,通过深入分析纠缠微波信号的特性,提出了两种纠缠微波信号的表示方法.一种是在量子框架下,利用双模压缩真空态表示,并分别在光子数表象下和Wigner分布下分析了其信号特征,刻画了正交分量之间的正反关联特性;另一种是在经典框架下,利用关联随机信号表示,刻画了测量后纠缠微波信号场幅度正交分量随时间变化的波形图.两种表示恰当合理地反映了纠缠微波信号连续变量纠缠的特性.     

Quantum Entanglement Dynamics of Two Atoms in Quantum Light Sources

Quantum entanglement dynamics of two Tavis-Cummings atoms interacting with the quantum light sources in a cavity is investigated. The results show the phenomenon that the concurrence disappears abruptly in a finite time, which depends on the initial atomic states and the properties of squeezed states. We find that there are two decoherence-free states in squeezed vacuum fields: one is the singlet state, and the other entangled state is the state
that combines both excited states and ground states with a relative phase being equal to the phase of the squeezed state.     

Continuous-variable Entanglement in a Correlated Spontaneous Emission Laser

We discuss the generation and evolution of entangled light in a correlated spontaneous emission laser in the linear regime. The master equation for the two-mode cavity field is derived and solved analytically in phase space. The time-dependent characteristic function in the Wigner representation for the two-mode field is obtained. It shows that the two-mode field in the cavity evolves in a two-mode Gaussian state. The entanglement degree of the two- mode field in the cavity increases initially, then decreases, and finally vanishes as the field evolves from an initial vacuum. The period of the entanglement is extended as the intensity of the driving field is increased. It is found that the entanglement still exists even when the two-mode squeezing disappears. During the entanglement period, the intensity of the field is amplified. The entanglement for the initial field being a two-mode squeezed vacuum and the entanglement of the output field are also discussed.     

Generation of Entanglement Between Two Noninteracting Qubits via Interaction with Nonclassical Radiation Field

We study the interaction between a single-mode quantized field and a quantum system composed of two qubits. We suppose that two qubits initially be prepared in the mixed and separable state, and study how entanglement between two qubits arises in the course of evolution according to the Jaynes-Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem. When the qubits are initially prepared in the maximally mixed and separable state, for coherent state field we cannot find entanglement between two qubits; for squeezed state field entanglement between two qubits exists in several short period of time; for even and odd coherent state fields of large photon number, the dynamical behavior of the entanglement between two qubits shows collapse and revival phenomenon. For odd coherent state field of small photon number, the entanglement with both qubits initially prepared in maximally mixed state can be stronger than that with both qubits initially prepared in pure states. For fields of small photon number, the entanglement strongly depends on the states they are initially prepared in. For coherent state field, and odd and even coherent state fields of large photon number, the entanglement only depends on the purity of the initial state of qubit subsystem. We also show that during the evolution the unentangled state may be purer than the entangled state, and the maximum degree of entanglement may not occur at the time when the qubit subsystem is in the purist state.     

Entanglement,BEC, and superfluid-like behavior of two-mode photon systems

A system of two interacting photon modes, without constraints on the photon number, in the presence of a Kerr nonlinearity, exhibits BEC if the transfer amplitude is greater than the mode frequency. A symmetry-breaking field (SBF) can be introduced by taking into account a classical electron current. The ground state, in the limit of small nonlinearity, becomes a squeezed state, and thus the modes become entangled. The smaller is the SBF, the greater is entanglement. Superfluid-like behavior is observed in the study of entanglement growth from an initial coherent state, since in the short-time range the growth does not depend on the SBF amplitude, and on the initial state amplitude. On the other hand, the latter is the only parameter which determines entanglement in the absence of the SBF.     

Generation of Entanglement Between Two Noninteracting Qubits via Interaction with Nonclassical Radiation Field

We study the interaction between a single-mode quantized field and a quantum system composed of two qubits. We suppose that two qubits initially be prepared in the mixed and separable state, and study how entanglement between two qubits arises in the course of evolution according to the Jaynes-Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem. When the qubits are initially prepared in the maximally mixed and separable state, for coherent state field we cannot find entanglement between two qubits; for squeezed state field entanglement between two qubits exists in several short period of time; for even and odd coherent state fields of large photon number, the dynamical behavior of the entanglement between two qubits shows collapse and revival phenomenon. For odd coherent state field of small photon number, the entanglement with both qubits initially prepared in maximally mixed state can be stronger than that with both qubits initially prepared in pure states. For fields of small photon number, the entanglement strongly depends on the states they are initially prepared in. For coherent state field, and odd and even coherent state fields of large photon number, the entanglement only depends on the purity of the initial state of qubit subsystem. We also show that during the evolution the unentangled state may be purer than the entangled state, and the maximum degree of entanglement may not occur at the time when the qubit subsystem is in the purist state.     

Amplification of entangled states of squeezed light

Two amplification schemes are considered for entangled squeezed states of light, including an Einstein-Podolsky-Rosen entangled state of continuous variables (EPR pair): propagation in a nonlinear medium and reflection from a cavity. Both schemes make use of a parametric process that can be implemented in a periodic nonlinear medium. The existence of an integral of motion makes it possible to amplify an entangled state of light while preserving the initial entanglement. To analyze the cavity-based scheme, a master equation is derived for the density matrix of the field inside the cavity. The feasibility of amplification that preserves entanglement of an EPR pair is demonstrated for this scheme.     

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.     

Entanglement swapping between electromagnetic field modes and matter qubits

Scalable quantum networks require the capability to create, store and distribute entanglement among distant nodes (atoms, trapped ions, charge and spin qubits built on quantum dots, etc.) by means of photonic channels. We show how the entanglement between qubits and electromagnetic field modes allows generation of entangled states of remotely located qubits. We present analytical calculations of linear entropy and the density matrix for the entangled qubits for the system described by the Jaynes-Cummings model. We also discuss the influence of decoherence. The presented scheme is able to drive an initially separable state of two qubits into an highly entangled state suitable for quantum information processing.     

Effects of Cavity-Field Statistics on Atomic Entanglement in Two-Mode Jaynes-Cummings Model

We study the entanglement properties of a pair of two-level Rydberg atoms passing one after another into a lossless cavity with two modes. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the cavity field results in the final two-atom mixed entangled type state. The entanglement of formation of the joint two-atom state as a function of the Rabi angle gt is calculated for Fock state field, coherent field and thermal field respectively inside the cavity. We present a comparative study of two-atom entanglement corresponding to the different field statistics.     

Extended entanglement to quantum networks

Connecting individual quantum systems through quantum channels leads to develop quantum networks crucial to perform multipartite communication or quantum cryptography. We present two techniques to generate entanglement among different parties at larger scale. In the first approach cavity QED technique is used to produce extended entanglement in atomic internal and external degrees of freedom. In this scheme we entangle two tagged atoms in their momentum state with cavity fields. Later, interaction of two auxiliary atoms with the two cavity fields in non-dispersive and dispersive fashion transforms the atoms–fields entanglement to atoms–atoms entanglement. Quantum measurement on auxiliary atoms generates extended entangled state in atomic degrees of freedom. In the second approach we take three cavities in which the two cavities have separate entangled state with third cavity in two modes which are distinguishable. Applying quantum measurement process on third cavity, we develop extended entangled state among the three cavities. We provide experimental parameters to realize the work in laboratory experiment.     

Bright entangled light from two-mode cascade laser

We show that a two-mode three-level cascade laser driven by external coherent fields generate intense entangled light. It turns out that external driving fields which are at resonance with the cavity modes substantially improve the intensity of the two-mode light in the cavity in a region where the squeezing and entanglement is significant making the system under consideration a viable source of bright squeezed as well as entangled light.