Environment induced entanglement in cavity-QED

The effects of dissipative dynamics on the magnitude of entanglement generated In atom-photon interactions inside cavities is studied. We present some concrete examples of environment Induced entanglement in alom-photon interactions. We consider various dissipative atom-cavity systems and show that their collective dynamics can be used to maximize entanglement for intermediate values of the cavity leakage parameter κ. We first consider the interaction of a single two-level atom with one of two coupled microwave cavities and show analytically that the atom-cavity entanglement increases with cavity leakage. We next consider a system of two atoms passing successively through a cavity and derive the expression for the maximum value of in terms of the Rabi angle gt, for which the two-atom entanglement can be Increased. Finally, numerical investigation of micromaser dynamics also reveals the increase of two-atom entanglement with stronger cavity-environment coupling for experimentally attainable values of the micromaser parameters.     

原子与耦合腔相互作用系统中的纠缠特性

研究了耦合腔A和B中各囚禁一个二能级原子的情况,给出了总激发数为2时系统态矢的演化.利用Negativity熵度量两子系统间的纠缠,采用数值计算方法研究了两个原子之间、腔内原子与腔场之间和两个腔场之间的纠缠性质.讨论了腔场间的耦合强度对纠缠特性的影响.研究结果表明:原子1和原子2处于分离态.另一方面,随腔场间耦合系数增大腔场间的纠缠和原子与腔场间的纠缠减小.     

原子与耦合腔相互作用系统中的纠缠特性

研究了耦合腔A和B中各囚禁一个二能级原子的情况,给出了总激发数为2时系统态矢的演化.利用Negativity熵度量两子系统间的纠缠,采用数值计算方法研究了两个原子之间、腔内原子与腔场之间和两个腔场之间的纠缠性质.讨论了腔场间的耦合强度对纠缠特性的影响.研究结果表明:原子1和原子2处于分离态.另一方面,随腔场间耦合系数增大腔场间的纠缠和原子与腔场间的纠缠减小.     

Entanglement Properties in the System of Three Atoms Trapped in Three Distant Cavities Connected by Two Optical Fibers

This paper discusses the entanglement dynamics of a coupled cavity quantum electrodynamics (CQED) setup, which comprises three two-level atoms resonantly interacting with three cavities that are coupled by two optical fibers. The influences of atom-cavity coupling constant on the entanglement between atoms and that between cavities are discussed. The results obtained from the numerical method show that the entanglement between non-adjacent atoms or that between adjacent cavities has a nonlinear relation with increasing of the atom-cavity coupling coefficient. On the other hand, the entanglement between non-adjacent cavities is strengthened and the entanglement between adjacent atoms is weakened with increasing of atom-cavity coupling constant.     

三个耦合腔系统中的纠缠特性

本文研究将三个二能级原子分别囚禁在耦合腔A, B和C中, 腔中原子与腔场发生共振相互作用的情况. 采用Negativity熵度量两子系统间的纠缠, 通过数值计算给出了两个原子之间和两个腔场之间的纠缠演化. 讨论了腔场间的耦合强度对纠缠特性的影响. 研究结果表明: 原子间的纠缠与腔场间的耦合系数间存在非线性关系. 另一方面, 相邻腔场腔A和腔B间, 以及腔B和腔C间的纠缠随腔场间的耦合系数增大而减弱, 但非相邻腔场腔A和腔C间的纠缠却随腔场间的耦合系数增大而增强.     

双光子过程耦合腔系统中的纠缠特性

研究了双光子过程原子与耦合腔相互作用系统,给出了系统总激发数等于2时态矢的演化。采用负本征值来描述两个子系统间的纠缠,利用数值计算方法研究了系统中原子与原子间、腔场与腔场间和原子与腔场间的纠缠特性。讨论了腔场间的耦合强度变化对纠缠特性的影响。研究结果表明:随着腔场间耦合的增强,两原子间的纠缠增强,但原子与腔场间和两腔场间的纠缠却减弱。     

The Entanglement Properties Induced by Atoms in Two Separate Cavities Connected by an Optical Fiber

We study the entanglement evolution between two atoms, which are initially entangled with a third atom and trapped in two separated cavities coupled by an optical fiber. We also investigate the temporal evolution in the entanglement between the atom and the local cavity mode. The influence of the state-selective measurement on the atom outside the cavities and the influence of cavity-fiber coupling coefficient on the entanglement are discussed. The results show that the entanglement can be strengthened through the state-selective measurement on the atom outside the cavities. We also find that, by increasing the cavity-fiber coupling coefficient, the atom-atom entanglement is strengthened, but the atom-cavity entanglement is weakened.     

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.     

Entanglement Properties in a Star Structure Coupled Cavities System

In this paper, the star structure coupled cavities system is composed of six single-mode cavities. One of them is at the center of the star structure, and other five cavities are at the five vertices of the star structure, respectively. The center cavity is connected with other five cavities by optical fibers. The situation is considered that six identical two-level atoms are separately trapped in six single-mode optical cavities, each atom resonantly interacts with cavity via a one-photon hopping, and the total excitation number of the system equals one. Negativity is adopted to quantify the degree of entanglement between two subsystems. The entanglement properties between atoms and that between cavities are investigated. The influences of atom-cavity coupling coefficient on the entanglement properties between two subsystems are studied. The results obtained using the numerical method show that the atom-atom entanglement is weakened, and the cavity-cavity entanglement is strengthened with the increase of atom-cavity coupling coefficient.

     

Transferring quantum entangled states between multiple single-photon-state qubits and coherent-state qubits in circuit QED

We present a way to transfer maximally- or partially-entangled states of n single-photon-state (SPS) qubits onto ncoherent-state (CS) qubits, by employing 2nmicrowave cavities coupled to a superconducting flux qutrit. The two logic states of a SPS qubit here are represented by the vacuum state and the single-photon state of a cavity, while the two logic states of a CS qubit are encoded with two coherent states of a cavity. Because of using only one superconducting qutrit as the coupler, the circuit architecture is significantly simplified. The operation time for the state transfer does not increase with the increasing of the number of qubits. When the dissipation of the system is negligible, the quantum state can be transferred in a deterministic way since no measurement is required. Furthermore, the higher-energy intermediate level of the coupler qutrit is not excited during the entire operation and thus decoherence from the qutrit is greatly suppressed. As a specific example, we numerically demonstrate that the high-fidelity transfer of a Bell state of two SPS qubits onto two CS qubits is achievable within the present-day circuit QED technology. Finally, it is worthy to note that when the dissipation is negligible, entangled states of n CS qubits can be transferred back onto n SPS qubits by performing reverse operations. This proposal is quite general and can be extended to accomplish the same task, by employing a natural or artificial atom to couple 2nmicrowave or optical cavities.     

The Influences of the Selective Atomic Measurement on Entanglement Properties in the System of Three Atoms Trapped in Two Distant Cavities Connected by an Optical Fiber

Three two-level atoms are trapped in two initially empty cavities connected by an optical fiber. The entanglement evolution between two atoms in the same cavity and the entanglement evolution between two cavities are investigated. The influence of the state-selective measurement of the atom trapped in the other cavity on the entanglement and that of fiber-cavity coupling coefficient on the entanglement are discussed. The results obtained show that atom-atom entanglement property is strengthened, and cavity-cavity entanglement property is weakened with increasing of the cavity-fiber coupling coefficient. On the other hand, the results also show that the entanglement between two cavities and that between two atoms in the same cavity can be strengthened through the state-selective measurement on the atom trapped in the other cavity.     

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.     

Qubit movement-assisted entanglement swapping

We propose a scheme to generate entanglement between two distant qubits(two-level atom) which are separately trapped in their own(in general) non-Markovian dissipative cavities by utilizing entangling swapping, considering the case in which the qubits can move along their cavity axes rather than a static state of motion. We first examine the role of movement of the qubit by studying the entropy evolution for each subsystem. The average entropy over the initial states of the qubit is calculated. Then by performing a Bell state measurement on the fields leaving the cavities, we swap the entanglement between qubit-field in each cavity into qubit-qubit and field-field subsystems. The entangling power is used to measure the average amount of swapped entanglement over all possible pure initial states. Our results are presented in two weak and strong coupling regimes, illustrating the positive role of movement of the qubits on the swapped entanglement.It is revealed that by considering certain conditions for the initial state of qubits, it is possible to achieve a maximally long-leaving stationary entanglement(Bell state) which is entirely independent of the environmental variables as well as the velocity of qubits. This happens when the two qubits have the same velocities.     

Squeezing‐Enhanced Atom–Cavity Interaction in Coupled Cavities with High Dissipation Rates

The realization of the strong coupling regime is requisite for implementing quantum information tasks. Here, a method for enhancing the atom–field coupling in highly dissipative coupled cavities is proposed. By introducing parametric squeezing into the primary cavity, which is only virtually excited under specific parametric conditions, coupling enhancement between the atom and the auxiliary cavity is realized for appropriate squeezing parameters. This enables the system to be robust against large cavity decay and atomic spontaneous emission. The observation of vacuum Rabi oscillations show that the originally weakly coupled system can be enhanced into an effective strong coupling regime.     

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     

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.     

耦合腔系统中的三体纠缠演化

研究由耦合腔和四个全同的二能级原子构成的系统中三体纠缠态纠缠量的演化. 四个原子分别囚禁在单模耦合腔A和B中, 并且原子通过单光子跃迁与腔场发生共振相互作用. 采用纠缠张量方法, 通过数值计算研究了每个腔中三体纠缠的演化. 讨论了原子与腔场间的耦合强度对三体纠缠演化的影响. 研究结果表明: 原子与腔场间的两体纠缠强于原子间的两体纠缠, 每个腔中的三体纠缠是两体纠缠相干叠加的结果.     

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.     

原子与耦合腔相互作用系统中的纠缠特性

本文研究将两个二能级原子分别注入耦合腔A和B中,并且原子与腔场发生共振相互作用的情况.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、腔内原子与腔场之间和两个腔场之间的纠缠性质.讨论了腔场间的耦合强度对纠缠特性的影响.研究结果表明:随腔场间耦合的增强,两原子间的纠缠增强,而原子与腔场间和两腔场间的纠缠减弱. 关键词： 量子光学 二能级原子 耦合腔 量子纠缠     

原子与耦合腔相互作用系统中的量子失协

本文研究由两个全同的二能级原子和耦合腔构成的系统,利用Dakic等提出的几何量子失协的度量方法,采用数值计算方法计算了系统中两原子间和两腔场间量子失协的演化.讨论了原子间初始纠缠度和腔场间耦合系数变化对几何量子失协演化的影响.研究发现:随腔场间耦合系数的增大,量子失协周期性演化的频率增大;随原子间初始纠缠度的增大,两原子间的关联增强,两腔场间的关联减弱.