Quantum Entanglement in a System of Two Spatially Separated Atoms Coupled to the Thermal Reservoir

We study quantum entanglement between two spatially separated atoms coupled to the thermal reservoir. The influences of the initial state of the system, the atomic frequency difference and the mean number of the thermal field on the entanglement are examined. The results show that the maximum of the entanglement obtained with nonidentical atoms is greater than that obtained with identical atoms. The degree of entanglement is progressively decreased with the increase of the thermal noise. Interestingly, the two atoms can be easily entangled even when the two atoms are initially prepared in the most mixed states.     

Entanglement between two qubits interacting with a slightly detuned thermal field

In this paper, we investigate entanglement between two two-level atoms when they simultaneously interact with a single-mode thermal field in the strong-coupling regime. We show that a slight detuning between the atomic transition frequency and the field frequency might cause high entanglement between the atoms. More interestingly, if we choose the detuning appropriately, both atoms would somehow get entangled even when both atoms are initially in the excited state.     

Control and Transfer of Entanglement between Two Atoms Driven by Classical Fields under Dressed-State Representation

We have studied the dynamics and transfer of the entanglement of the two identical atoms simultaneously interacting with vacuum field by employing the dressed-state representation. The two atoms are driven by classical fields. The influence of the initial entanglement degree of two atoms, the coupling strength between the atom and the classical field and the detuning between the atomic transition frequency and the frequency of classical field on the entanglement and atomic linear entropy is discussed. The initial entanglement of the two atoms can be transferred into the entanglement between the atom and cavity field when the dissipation is neglected. The maximally entangled state between the atoms and cavity field can be obtained under some certain conditions. The time of disentanglement of two atoms can be controlled and manipulated by adjusting the detuning and classical driving fields. Moreover, the larger the cavity decay rate is, the more quickly the entanglement of the two atoms decays.     

Concentration of Unknown Atomic Entangled States via Entanglement Swapping through Raman Interaction

We show that entanglement concentration of unknown atomic entangled states is achieved via the implementation of entanglement swapping based on Raman interaction in cavity QED. A maximally entangled state is obtained from a pair of partially entangled states probabilistically. Due to Raman interaction of two atoms with a cavity mode and an external driving field, the influence of atomic spontaneous emission has been eliminated. Because of the virtual excitation of the cavity mode, the decoherence of cavity decay and thermal field is neglected.     

Entangling Two Multi-atomic Clusters Through a Cavity Field

Two atomic clusters, which have NA and Ns two-level atoms, respectively, are placed in a cavity but separated spatially. There is no direct interaction between the atoms. All the atoms interact with a single-mode of the cavity field. Quantum entanglement between the two atomic clusters is investigated for various initial states of the two atomic clusters and the field. When the cavity field is initially in a Fock state, we find that the time evolution of entanglement quasi-periodically oscillates regardless of the initial states of atoms. The oscillation period increases as the initial photon number increases. When all the atoms in both of the atomic clusters are initially in the excited state, we show that there is no entanglement between the atomic clusters with NA = NB = 1 regardless the initial state of the cavity field. However, when either NA or NB is larger than one, we find that the entanglement always exists even for a strong thermal field. In cases with different initial states of the atomic clusters, we notice that the entanglement becomes stronger as number of the atoms increases. When all the atoms in both of the clusters in the ground state, we also find that the entanglement can be enhanced even by a thermal field. We also notice that a single qubit can be entangled with multi-atoms which are initially in the ground state by the cavity field initially being in vacuum, thermal, coherent, and squeezed states.     

Thermal Entanglement Between a Jaynes-Cummings Atom and an Isolated Atom

We studied the entanglement of a quantum system consisting of a Jaynes-Cummings atom, thermal lossless cavity and an isolated atom. The analytical expressions of the atom-atom negativity for separable and entangled initial atomic states were obtained. The influence of a detuning between the atomic transition frequency and the field frequency and direct dipole-dipole interaction on an atom-atom entanglement is examined. We showed that for a separable initial atomic states a detuning might cause high atom-atom entanglement in the presence of the dipole-dipole interaction. We also obtained that for an entangled initial atomic state a detuning causes a stabilization of an entanglement oscillations both for model with dipole-dipole interaction and model without such interaction.     

Entanglement properties between two atoms in the binomial optical field interacting with two entangled atoms

The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.     

Entanglement dynamics of spatially close bipartite atomic systems in thermal environment

We investigate the entanglement dynamics in a bipartite atomic system subjected to thermal environment with arbitrary initial pure entangled states. We consider the atoms close together and study the effect of temperature of the reservoir and the interatomic distance on the evolution of entanglement for both initially entangled and unentangled states. We find that we can have long time entanglement even in thermal environment.     

Quantum entanglement in the system of two two-level atoms interacting with a single-mode vacuum field

The entanglement properties of the system of two two-level atoms interacting with a single-mode vacuum field are explored. The quantum entanglement between two two-level atoms and a single-mode vacuum field is investigated by using the quantum reduced entropy; the quantum entanglement between two two-level atoms, and that between a single two-level atom and a single-mode vacuum field are studied in terms of the quantum relative entropy. The influences of the atomic dipole--dipole interaction on the quantum entanglement of the system are also discussed. Our results show that three entangled states of two atoms--field, atom--atom, and atom--field can be prepared via two two-level atoms interacting with a single-mode vacuum field.     

A Theoretical Scheme for Entanglement Transfer under Intensity-Dependent Couplings

We consider a theoretical scheme for entanglement transfer between a two-mode squeezed vacuum field and two initially separable atoms through intensity-dependent couplings. We find that the entanglement transfer between the field and the atoms has an exact period for any given squeezing. We also find that the maximum achievable entanglement of the atomic subsystem is a simple increasing function of r.For sufficiently large squeezing parameter r, it is possible for the atoms to be entangled into a Bell state at half the periodic time points.     

双纠缠原子在耗散腔场中的纠缠动力学

研究了能量损耗腔中,两纠缠二能级原子与单模辐射场相互作用过程中原子的纠缠动力学.结果表明:双纠缠原子的纠缠度演化特性决定于初始两原子间的纠缠度、纠缠形式、腔场的平均光数、腔场的衰变系数.当原子初始处于一特定纠缠态时,其纠缠度可以放大,并且不受腔场损耗的影响. 关键词： 二能级原子 纠缠度 密度算符 单模辐射场     

Effect of mode mode-competition on atom-atom entanglement

A system consisting of two atoms interacting with a two-mode vacuum is considered, where each atom is resonant with the two cavity modes through two different competing transitions. The effect of mode--mode competition on the atom--atom entanglement is investigated. We find that the entanglement between the two atoms can be induced by the mode--mode competition. For the initial atomic state |\varPsi(0)\rangle, whether the atoms are initially separated or entangled, a large or even maximal entanglement between them can be obtained periodically by introducing the mode--mode competition. For the initial atomic state |\varPhi(0)\rangle, the strong mode--mode competition can prevent the two atoms entangled initially from suffering entanglement sudden death; besides, it makes them in a more stable and longer-lived entanglement than in the non-competition case.     

Evolution of Atomic Entanglement for Different Cavity-Field Statistics in Single-Mode Two-Photon Process

We study the evolution of entanglement for a pair of two-level Rydberg atoms passing one after another into an ideal cavity filled with a single mode radiation field. The atoms interact with the cavity field via two-photon transitions. The initial joint state of two atoms that enter the cavity one after the other is unentangled. Interactions intervened by the single mode cavity photon field brings out the final two-atom mixed entangled type state. We use the well known measure appropriate for the mixed states, i.e. the entanglement of formation to quantify the entanglement. We calculate the entanglement of formation of the joint two-atom state as a function of the Rabi angle, for the Fock state field, coherent field and thermal field respectively inside the cavity. The change in the magnitude of atomic entanglement with cavity photon number has been discussed.     

两纠缠原子与相干态光场相互作用的动力学

采用时间演化算符和数值计算方法,研究了两全同二能级纠缠原子与相干态光场相互作用的动力学,结果表明:原子布居和偶极压缩特性与两原子体系纠缠度和相干态光场强度相关联.     

Spontaneously created entanglement between two atoms

Spontaneous emission as a potential tool for creation of entanglement between two atoms is investigated. We assume that the atoms are coupled to the same environment and study entanglement engineering between the atoms and its transfer between different states. The role of the atomic coherence induced by spontaneous emission will be explored which, in contrast to what is generally believed, can create entanglement between initially unentangled atoms. We quantify entanglement by the concurrence and find that it exhibits threshold properties that can lead to interesting noncontinuous phenomena of sudden birth and sudden death of entanglement. In addition, we consider the mechanism involved in creation of entanglement between distant atoms coupled to a single-mode cavity field. We include a possible variation of the coupling constants between the atoms and the cavity mode with location of the atoms in a standing-wave cavity mode. Effectively, we engineer two coupled atoms whose the dynamics are analogous to that of interacting and collectively damped two nonidentical atoms. We illustrate the interesting result that spatial variations of the coupling constants can lead to a stationary entanglement between the atoms. We explain this effect in terms of the trapping phenomenon of atomic population in a non-decaying entangled state.     

Tavis-Cummings模型中三体纠缠态纠缠量的演化特性

研究两个全同二能级原子与单模场相互作用的Tavis-Cummings模型中的量子纠缠.在场和两原子初始分别为真空场和纠缠或非纠缠状态下，得出体系状态将演化为三体近似W纠缠态.通过对纠缠量的计算得出：该三体近似W纠缠态纠缠量的演化特性将随三体所处的初始状态、原子间及原子与场间的耦合系数、失谐程度、原子反转粒子数的变化而变化.值得一提的是可得出原子间耦合作用强度对纠缠量的非线性效应，并且纠缠量展现出与原子反转粒子数一致的周期振荡现象. 关键词： W纠缠态 纠缠量 反转粒子数     

Entropy evolvement properties in a system of Schrodinger cat state light field interacting with two entangled atoms

The field entropy can be regarded as a measurement of the degree of entanglement between the light field and the atoms of a system which is composed of two-level atoms initially in an entangled state interacting with the Schr\"{o}dinger cat state. The influences of the strength of light field and the phase angle between the two coherent states on the field entropy are discussed by using numerical calculations. The result shows that when the strength of light field is large enough the field entropy is not zero and the degrees of entanglement between the atoms and the three different states of the light fields are equal. When the strength of the light field is small, the degree of entanglement is maximum in a system of the two entangled atoms interacting with an odd coherent state; it is intermediate for a system of the two entangled atoms interacting with the Yurke--Stoler coherent state, and it is minimum in a system of the two entangled atoms interacting with an even coherent state.     

Preparation and control of entangled states in the two-mode coherent fields interacting with a moving atom via two-photon process

We investigate the preparation and the control of entangled states in a system with the two-mode coherent fields interacting with a moving two-level atom via the two-photon transition. We discuss entanglement properties between the two-mode coherent fields and a moving two-level atom by using the quantum reduced entropy, and those between the two-mode coherent fields by using the quantum relative entropy. In addition, we examine the influences of the atomic motion and field-mode structure parameter $p$ on the quantum entanglement of the system. Our results show that the period and the duration of the prepared maximal atom-field entangled states and the frequency of maximal two-mode field entangled states can be controlled, and that a sustained entangled state of the two-mode field, which is independent of atomic motion and the evolution time, can be obtained, by choosing appropriately the parameters of atomic motion, field-mode structure, initial state and interaction time of the system.     

Generating controllable atom-light entanglement with a Raman atom laser system

We introduce a scheme for creating continuous variable entanglement between an atomic beam and an optical field, by using squeezed light to outcouple atoms from a Bose-Einstein condensate via a Raman transition. We model the full multimode dynamics of the atom laser beam and the squeezed optical field and show that, with appropriate two-photon detuning and two-photon Rabi frequency, the transmitted light is entangled in amplitude and phase with the outcoupled atom laser beam. The degree of entanglement is controllable via changes in the two-photon Rabi frequency of the outcoupling process.     

原子与热库相互作用系统中的三体纠缠特性

利用Ket-Bra纠缠态方法,求解了原子与热库相互作用系统中的密度矩阵主方程,得到了密度矩阵的演化表达式.考虑三个二能级原子独立与热库相互作用的情况,利用负本征值度量三体纠缠,研究了系统中原子间的三体纠缠特性.采用数值计算方法,讨论了热库平均光子数和原子自发辐射率对原子间三体纠缠特性的影响.研究结果表明:随原子自发辐射率和热库平均光子数的增大,原子间的三体纠缠衰减加快.