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.     

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.     

三纠缠原子与双模腔场相互作用系统的纠缠演化特性

研究了初始处于GHZ态的三个两能级原子与双模腔场相互作用系统的纠缠动力学特性,得到了并发度和线性熵的解析表达式.讨论了腔场初始纠缠度对腔内两原子之间纠缠的影响,对其余子系统求迹后结果表明腔内两原子之间的纠缠出现突然产生现象,腔内两原子之间产生纠缠的阈值时间和最大值依赖于双模腔场初始纠缠度;并且发现腔内两原子子系统和腔外原子与场子系统之间在整个的时间演化过程中一直保持着纠缠状态.     

控制Tavis-Cummings模型中两原子X态的纠缠突然死亡与突然产生

研究了初态为X态时Tavis-Cummings模型中具有偶极相互作用两原子的纠缠演化特性,在演化过程中,同时号码出现了两原子的纠缠突然死亡(ESD)与突然产生(ESB)两种有趣的现象.详细分析了两原子初始态的纯度、偶极相互作用、光场粒子数对这两种现象出现时间的影响,进一步给出了初始为混态时ESB与ESD的转换条件.计算结果表明,上述系统参量对两原子的纠缠演化、ESB与ESD有重要的影响,偶极相互作用会改变纠缠度的振荡周期,使出现ESD的时间间隔减少;随着初始两原子纠缠纯度的增大,纠缠突然产生以及纠缠突然死亡存在的时间缩短,并且可以提高两原子之间的纠缠;对于特殊的初态,产生了纠缠不变性以及固定的两原子纠缠,该定值受两原子初始状态的纯度控制。     

Controlling entanglement sudden death in cavity QED by classical driving fields

We investigate the entanglement dynamics of a quantum system consisting of two-level atoms interacting with vacuum or thermal fields with classical driving fields. We find that the entanglement of the system can be improved by adjusting the classical driving field. The influence of the classical field and the purity of the initial state on the entanglement sudden death is also studied. It is shown that the time of entanglement sudden death can be controlled by the classical driving fields. Particularly, the entanglement sudden death phenomenon will disappear if the classical driving fields are strong enough.     

Entanglement of Two Atoms Induced by a Fock State of Radiation Field

Considering the intrinsic decoherence proposed by Milburn, we investigate the entanglement between two two-level atoms induced by a Fock state of single-mode quantized radiation field. The time-dependent reduced density matrix of the atoms system is given explicitly. Due to the intrinsic decoherence, the atoms system will approach a stationary state, where the stationary entanglement depends on the initial states of the field and the atoms.     

腔量子电动力学系统中耦合三原子的纠缠特性

研究了三个全同二能级原子与单模腔相互作用系统中原子间的三体纠缠特性.考虑原子间存在相互耦合,并且腔场处于弱相干态的情况,通过数值计算给出了纠缠量的演化曲线,讨论了原子间耦合强度和弱相干场强度对三体纠缠的影响.研究结果表明:随弱相干场强度增强,原子间的三体纠缠增强;相反,随原子间耦合系数增大,原子间三体纠缠减弱.     

纠缠双原子对场熵压缩特性的影响

研究了相干态光场与纠缠双原子相互作用系统中场熵的压缩性质,借助于数值计算,讨论了双原子纠缠度及光场强度对场熵压缩的影响。所得结果表明,双原子初态的纠缠度对压缩的持续时间和压缩深度具有决定性的影响。当双原子初始时刻处于最大纠缠态时,场熵具有较大的压缩深度和较长的压缩时间。初始光场强度对场熵的压缩深度和压缩时间也具有显著的影响。光场愈弱,场熵的压缩性愈好。     

耗散腔场中两个∧型原子的纠缠特性

利用超算符方法求解幅值损耗腔中两个∧型三能级原子与相干光场相互作用系统的主方程,并利用量子条件熵研究了两个初始为|Ψa(0)＞和|Φa(0)＞纠缠态的原子与光场作用过程中原子的纠缠演化特性.讨论了不同初始原子纠缠度,不同耗散系数以及不同平均光子数对两原子纠缠度的影响.结果表明:①当原子初始处于|Ψa(0)＞类纠缠态时,其纠缠度随光场强度以及腔场衰减系数演化.当腔不存在耗散时,纠缠度呈周期性振荡;当腔存在耗散时,纠缠度呈衰减振荡并趋于稳定值;且光强越弱,其稳定值越大;衰减系数越大纠缠达到稳定值所需时间越短.②原子初始处于|Φa(0)＞类纠缠态时,其纠缠度只与原子初始纠缠度有关,不随其他因素变化.     

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.     

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     

Generation of fully three-mode continuous-variable entanglement in a single-atom laser

We proposed a scheme for generating fully three-mode continuous-variable (CV) entanglement between three nondegenerate cavity modes in a single-atom laser. In our scheme, the single-atom laser consists of a four-level atom inside a triply resonant cavity, and the atomic coherence is induced by two classical laser fields driving the corresponding atomic transitions. To demonstrate the generation of entanglement, we numerically simulated the dynamics of this system, and the numerical simulation shows that the single-atom laser considered here can be seen as a three-mode CV entanglement amplifier even in the presence of cavity losses. Moreover, we also show that the generation of entanglement doesn’t depend intensively on the initial condition of cavity field, and the fully three-mode CV entanglement can be realized no matter the three entangled (nondegenerate) modes are initially in the same state or different states based on our scheme.     

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.     

Entanglement Dynamics and Bell Violations of Two Atoms in Tavis-Cummings Model with Phase Decoherence

Considering the dipole-dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the system of two two-level atoms coupled to a single mode cavity in the presence of phase decoherence has been investigated. The two-atom entanglement appears with periodicity without considering phase decoherence, however, the phase decoherence causes the decay of entanglement between two atoms, with the increasing of the phase decoherence coefficient, the entanglement will quickly become a constant value, which is affected by the two-atom initial state. Meanwhile the two-atom quantum state will forever stay in the maximal entangled state when the initial state is proper even in the presence of phase decoherence. On the other hand, the Bell violation and the entanglement do not satisfy the monotonous relation, a large Bell violation implies the presence of a large amount of entanglement under certain conditions, while a large Bell violation corresponds to a little amount of entanglement in certain situations. However, the violation of Bell-CHSH inequality can reach the maximal value if two atoms are in the maximal entangled state, or vice versa.     

Enhancing entanglement generation of two atoms in a cavity with white noise using classical driving fields

We investigate the entanglement dynamics of a quantum system consisting of two two-level atoms in a cavity with classical driving fields in the presence of white noise.The cavity is initially prepared in the vacuum state.Generally,the entanglement of two atoms decreases with the intensity of the thermal fields and the coupling strength of the two-level atoms to the thermal fields.However,we find that the entanglement of the quantum system can be enhanced by adjusting the frequency and the strength of the classical driving fields in the presence of white noise.     

Quantum Entanglement in a Structured Reservoir

We study the entanglement dynamics of two-level atoms interacting in independent structured non-Markovian reservoirs. The atoms are initially prepared in a pure W state and the reservoir is in the vacuum. We have shown that the degree of entanglement of the initial states, Markovian environments can control the time of the two qubit entanglement sudden death and the reservoirs’ entanglement sudden birth. We show the dependence of entanglement dynamics on the non-Markovianity. When the initial state of atoms is in a pure W state, the entanglement will decay asymptotically.     

Entropy of field interacting with two two-qubit atoms

We use quantum field entropy to measure the degree of entanglement for a coherent state light field interacting with two atoms that are initially in an arbitrary two-qubit state. The influence of different mean photon number of the coherent field on the entropy of the field is discussed in detail when the two atoms are initially in one superposition state of the Bell states. The results show that the mean photon number of the light field can regulate the quantum entanglement between the atoms and light field.     

Entanglement for two-atom Tavis–Cummings model with degenerate two-photon transitions in the presence of the Stark shift

The dynamics of atom–field entanglement for two two-level atoms with degenerate two-photon transitions interacting with one-mode radiation field with taking into account the Stark shift is investigated. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent fields. The atom–field entanglement is investigated also on the basis of the linear atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process is shown. Conditions and times of disentanglement are derived.     

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.