Stationary State Entanglement of Two Atoms Inside an Optical Cavity under Noise

In this paper, the entanglement properties of a system of two atoms inside an optical cavity in a stochastic interaction with field are studied by the Jaynes-Cummings Model. The phase telegraph noise is considered as a noise term and an exact solution to the model is obtained. The solution reveals the resulting decoherence effects of the noise on the entanglement properties of the system. It shows that under the noise the individual atoms do not entangle with the cavity field. However, a strong atom-atom entanglement is observed in a stationary state. It is seen that a relatively strong noise is cooperative in the construction of the steady state atom-atom entanglement.     

弱相干场耦合腔系统中的纠缠特性

研究由三个全同的二能级原子与耦合腔构成的系统, 考虑腔场处于弱相干态的情况. 采用Negativity熵度量两子系统间的纠缠, 利用数值计算方法研究了两个原子之间和两个腔场之间的纠缠性质. 讨论了腔场间的耦合系数和腔场的强度对纠缠特性的影响. 研究结果表明: 随光场强度增大, 原子间纠缠和腔场间纠缠均增强. 另一方面, 随耦合腔的耦合系数增大, 两原子间的纠缠减弱, 腔A和腔B间的纠缠增强; 而腔B和腔C间的纠缠, 以及腔A和腔C间纠缠与腔场间的耦合系数间存在非线性关系.     

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.     

Entanglement dynamics of two atoms successively passing a cavity

By means of concurrence, we investigate the dynamics of entanglement between two initially separate atoms in succession passing through a cavity and their interaction with a Fock state field. We then analyze the effects of the atomic coherence, photon number, and atomic motion on the time evolution of atom-atom entanglement. The results show that there can be entanglement between two separate atoms, and that the threshold time for the creation of the entanglement is controllable by the photon number, atomic motion, and field-mode structure.     

Sudden Death and Long-Lived Entanglement Between Two Atoms in a Double JC Model System

Considering a double JC model with different coupling constants, we investigate the entanglement between the two two-level atoms, and discuss dependence of the atom-atom entanglement on the different coupling constants, and the detuning between the atomic transition frequency and the cavity field frequency. The results show when Δ=δ/g is small, with the increase of the relative difference of the two atom-cavity coupling constants γ, the atom-atom entanglement periodically evolves with the amplitude slowly and periodically modulated. What’s more interesting is that long-lived entanglement between the two atoms can be obtained when atom A non-resonantly interacts with the cavity field a, and atom B has no coupling with the cavity field b. In this case, the concurrence C ^AB (t) of the two atoms evolves in form of cosine, and is invariant and equals the initial value when far off resonance. In addition, we find that the so-called entanglement sudden death can occur under appropriate conditions on the detunings and the different coupling constants for different initial atomic states.     

Generation of maximally entangled atom pairs in driven dissipative cavity QED systems

We investigate the entanglement of an open tripartite system where a cavity field mode in thermal equilibrium is off-resonantly coupled with two atoms that are simultaneously driven by a resonant coherent field. For moderately detuned atom-field coupling and strong atomic driving we show the generation, at given interaction times and for low enough cavity decay rates, of atomic Bell states and of Bell state superpositions relevant for quantum gates implementation. The system can oscillate between bi-separable and fully separable states. Also we describe the distribution of quantum correlations between the atom-atom and the two atom-field subsystems. In the dispersive coupling regime with strongly driven atoms we show the generation of nearly stationary Bell states which remain protected from cavity dissipation.     

Entanglements induced by cavity interacting with two-coupled atoms

We consider a quantum optics model where the cavity interacts with two-coupled atoms. The atom-atom entanglement, atoms-cavity entanglement and the mixture for the two atoms are investigated, and discuss the effects of the initial conditions, atom-atom coupling and the mean number of photons on the entanglements and mixture. We find that atom-atom coupling plays an important role in the entanglement and mixture. Numerical results show that under some conditions the phenomena of “entanglement sudden death” and “entanglement collapse and revival” emerge.     

Sudden birth of entanglement between two atoms successively passing a thermal cavity

We study the dynamics of entanglement of two initially separate atoms passing through a cavity one after another by employing the concurrence and negativity. The effects of the atomic coherence and mean photon number on the time evolution of atom-atom entanglement are examined when the field is initially in thermal field. We show that the phenomenon of sudden birth of entanglement occurs in some certain conditions and the threshold time for the creation of the entanglement can be controlled by the atomic coherence and mean photon number of the field. It is also shown that the entanglement between two atoms can be created even if the two atoms are initially in excited states.     

Entanglement swapping in two independent Jaynes-Cummings models

We consider two independent Jaynes-Cummings models which consist of an atom interacts with electromagnetic field modes. The generation of atom-atom entanglement is investigated. No direct interaction between the two atoms exists. Entanglement can be created using entanglement swapping method by an interference measurement performed on photons. We discuss the influence of off-resonance and the initial state of the atom on the atom-atom entanglement. It is shown that the maximal atom-atom entanglement can be obtained and the atom-atom entanglement is sensitive to the off-resonance and the initial state of the atom.     

利用纠缠交换制备原子-原子最大纠缠态

基于腔量子电动力学(QED)提出一种利用两对纠缠的级联型三能级原子与单模腔场系统制备原子-原子最大纠缠态的简单方案,最初两原子之间、两腔场之间互不纠缠,使其中一个原子与一个腔场发生作用,即纠缠交换,该过程仅需对单个腔场态测量就可实现从未有直接作用的两个原子之间的纠缠,精确控制原子与腔场的相互作用时间可获得具有最大保真度的纠缠态.该方案可以延长腔的有效泄漏时间,从而能有效克服光腔的消相干的影响,这样大大降低了系统对腔的品质的要求.     

原子在弱相干场光纤耦合腔系统中的纠缠特性

研究由两个相同的二能级原子分别处于用单模光纤耦合的两弱相干光场系统的共生纠缠特性, 通过数值计算研究了光纤模-腔模与原子-腔模的耦合强度比、弱相干光场的强度和两光场相对相位差等因素对系统纠缠演化的影响. 结果表明: 两腔中的两原子之间、两光场之间和每个腔中的原子与光场之间的纠缠随时间呈现周期或准周期性演化, 两腔场之间的纠缠与腔中的两原子的纠缠可以相互转换, 与两原子之间和两光场之间的纠缠相比, 每个腔中光场与原子之间的纠缠随时间变化的周期缩短. 光纤模-腔模与原子-腔模的耦合强度比与两腔中光场相位差对系统纠缠的影响很大, 较小的光纤模-腔模与原子-腔模的耦合强度之比可以获得较大的系统纠缠度. 关键词： 弱相干场 光纤耦合腔 耦合强度 量子纠缠     

陆续通过一个双模腔的两原子之间纠缠的突然产生和调控

通过计算并发度研究了陆续通过一个双模腔的两个原子之间的纠缠动力学特性, 讨论了第一个原子的相干性以及腔场初始纠缠度对两原子之间纠缠的影响. 结果表明系统在一定条件下可以出现两原子之间纠缠突然产生现象, 两原子之间产生纠缠的最大值依赖于双模腔场初始纠缠度; 并且可以通过改变原子的振幅来控制产生纠缠的阈值时间和纠缠的最大值, 理论上提供了一种调控纠缠的方式.     

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.     

频率变化的光场对双J-C模型中原子-原子纠缠的调控

本文研究了频率随时间变化的光场对双J-C模型中原子--原子纠缠的动力学调控, 主要讨论了光场频率随时间作正弦变化和脉冲变化两种典型情况下, 原子--原子纠缠度随时间的演化特性. 当光场频率随时间作正弦变化时, 原子--原子纠缠度演化的周期、振幅与光场频率调制的振幅有关, 并随着调制振幅的增强而减小. 光场频率的正弦调制和脉冲调制均能使光场与原子的相互作用模式在共振和非共振之间发生变化, 直接影响原子--原子纠缠度的演化规律. 通过光场频率的调制可以实现原子--原子纠缠度的提高与稳定, 避免ESD现象的出现, 从而达到动态调控原子--原子纠缠的目的.     

Testing a Bell-type inequality with a micromaser

We propose a phase-sensitive micromaser setup to demonstrate experimentally a violation of a Bell-type inequality. The interaction of atoms with the cavity field produces entanglement between the atoms and the cavity photons and therefore also between the atoms. We derive a Bell-type inequality for the atom-atom correlations and show that it can be violated not only in an idealized model but also under realistic circumstances when various sources of additional randomness are accounted for. Among them are the energy dissipation in the resonator and the Poissonian arrival statistics of the atoms.Prof. F.P. Schäfer on the occasion of his 65th birthday.     

Entanglement Dynamics of Two V-type Atoms with Dipole–Dipole Interaction in Dissipative Cavity

In this work, a coupled system of two V-type atoms with dipole–dipole interaction in a dissipative single-mode cavity, which couples with an external environment, is studied. The analytical solution of this model is obtained by solving the time dependent Schrodinger equation after Hamiltonian of dissipative cavity is diagonalized by introducing a set of new creation and annihilation operators according to Fano theorem. It is also discussed in detail how the entanglement dynamics of different initial states are influenced by the cavity-environment coupling, the spontaneously generated interference (SGI) parameter, and the dipole–dipole interaction between two atoms . The results show that the SGI parameter has different effects on entanglement dynamics under different initial states. Namely, the SGI parameter will increase the decay rate of the initially maximal entangled state and reduce that of the initially partial entangled state. For the initially product state, the larger SGI parameter corresponds to the more entanglement generated. The entanglement monotonically decreases under the weak cavity-environment coupling, while the oscillation of entanglement will occur under the strong cavity-environment coupling. The larger the dipole–dipole interaction is, the slower the entanglement decays and the more the entanglement will be generated. So the dipole–dipole interaction can not only protect and generate entanglement very effectively, but also enhance the regulation effect of the SGI parameter on entanglement.     

Quantum Entanglement and Quantum Discord of a Two-Qubit System in a Dissipative Cavity

The goal of this work is to investigate quantum entanglement and quantum discord of a pair of two-level atoms which is driven by an external classical field and interacts with a cavity field. After extracting density matrix of the atom-atom subsystem, it is shown that we have stronger quantum discord by increasing atom-field coupling constant for the case in which there is no entanglement. Moreover, for the atom-atom subsystem it is realized that quantum entanglement and quantum discord cannot increase, they decrease after passing some times due to cavity dissipation. Also quantum entanglement and quantum discord decrease faster by increasing atom-field coupling constant.     

原子与弱相干腔场相互作用系统中的量子特性

考虑腔场处于弱相干态的情况,研究了两个全同的二能级原子与耦合腔相互作用系统中原子的偶极压缩和原子间的纠缠特性。研究结果表明,随耦合腔耦合系数增大,原子的偶极压缩减弱。另一方面,随耦合腔耦合系数增大,原子间的纠缠也减弱,这一结果与耦合腔处于真空态的情况相反。     

Entropy evolution properties in a system of two entangled atoms interacting with light field

In this paper, we use the field entropy as a measurement of the degree of entanglement between the light field and the atoms of the system which is composed of two dipole—dipole interacting two-level atoms initially in an entangled state interacting with the single mode coherent field in a Kerr medium. The influence of the coupling constant of dipole—dipole interaction between atoms and the coupling strength of the Kerr medium with the light field and the intensity of the light field on the field entropy are discussed by numerical calculations. It is shown that when the coupling strength of the Kerr medium with the light field is large enough, and the light field is strong, the degree of entanglement between the atoms with the light field becomes weaker. The degree of entanglement only changes slightly with the change of the coupling constant of dipole—dipole interaction between atoms.     

Entanglement Evolution Between Various Subsystems of Two Three-level Atoms Interacting with a Two-mode Quantized Field in the Presence of Converter Terms

In this paper, we study the interaction between two Λ-type three-level atoms (a typical qutrit-qutrit system) and two coupled modes of a quantized radiation field in the presence of field-field interaction (parametric down conversion) which are simultaneously injected within an optical cavity. Then, by applying an appropriate canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Under particular initial conditions for atoms (in some possible states) and the fields (in the finite dimensional pair coherent state) which may be prepared, the explicit form of the state vector of the whole system is analytically evaluated. In order to find the degree of entanglement between different parts of subsystems (“atom+atom”-field, “atom+field”-atom and atom-atom) the dynamics of entanglement through different measures, namely, linear entropy and negativity is evaluated. In each case, the effect of various types of initial atomic states on the above measures are numerically analyzed, in detail. It is indicated that the amount of entanglement can be tuned by choosing appropriate initial states of atoms. Particularly, it is shown that the entanglement sudden death (ESD) can be controlled by adjusting the initial state of the atoms.