Entanglement Dynamics of Two Atoms in the Squeezed Vacuum and the Coherent Fields

We investigate the entanglement dynamics of two atoms in a double damping Jaynes-Cummings model. The two atoms are initially in the Bell states and each is in a squeezed vacuum cavity field or coherent cavity field. Compared with the case in coherent field, the atomic entanglement in the squeezed vacuum field is stronger under the same conditions. The results show that we can adopt appropriate parameters such as mean photon number, detuning, the atomic spontaneous decay and the cavity decay, to realize better control of atomic entanglement in quantum information processing. What’s worth mentioning is that proper choosing of the last two parameters enables us to decrease disentanglement period and postpone the moment when the entanglement disappears. Finally, the atomic entanglement in double damping and non-identical Jaynes-Cummings model is obtained

     

Robust and fragile Werner states in the collective dephasing

We investigate the concurrence and Bell violation of the standard Werner state or Werner-like states in the presence of collective dephasing. It is shown that the standard Werner state and certain kinds of Werner-like states are robust against the collective dephasing, and some kinds of Werner-like states is fragile and becomes completely disentangled in a finite-time. The threshold time of complete disentanglement of the fragile Werner-like states is given. The influence of external driving field on the finite-time disentanglement of the standard Werner state or Werner-like states is discussed. Furthermore, we present a simple method to control the stationary state entanglement and Bell violation of two qubits. Finally, we show that the theoretical calculations of fidelity based on the initial Werner state assumption well agree with previous experimental results.     

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.     

Entanglement Evolution of a Two-Qubit System beyond Rotating-Wave Approximation

Two noninteracting qubits, initially entangled in Bell states, are coupled to a one-mode cavity and evolve under its influence. The entanglement evolution of the two qubits is investigated beyond the rotating-wave approximation. It is shown that the counter-rotating wave terms have a great influence on the disentanglement behavior.     

Concurrence evolution of two qubits coupled with one-mode cavity separately

The concurrence evolution of two qubits coupled with one-mode cavity separately is investigated exactly without adopting the rotating-wave approximation. The results show that for the resonant case, the concurrence evolution behaviour of the system is similar to that of the Markovian case when the coupling strength is weak, while the concurrence vanishes in a finite time and might revive fractional initial entanglement before it permanently vanishes when the coupling strength is strong. And for the detuning case, the entanglement could periodically recover after complete disentanglement. These results are quite different from those of system subjected to Jaynes--Cummings model.     

Modulation of entanglement and quantum discord for circuit cavity QED states

The paper investigates the dynamic evolution behaviors of entanglement and quantum discord of coupled superconducting qubits in circuit QED system. We put emphasis on the effects of cavity field quantum state on quantum entanglement and quantum correlations dynamic behaviors of coupling superconducting qubits. The results show that, (1) generally speaking, the entanglement will appear the death and new birth because of the interaction between qubits and cavity field, on the contrary, this phenomenon will not appear in quantum discord. (2) When the cavity field is in coherent state, the entanglement survival time is controlled by the average photon number. The more the average photon number is, the longer survival time of entanglement is prolonged. Thus it has the benefit of keeping quantum correlations. (3) When the cavity field is in squeezed state, the squeezed amplitude parameters have controlling effects on quantum correlations including entanglement and quantum discord. On the one hand, the increase of squeezed amplitude parameters can prolong the survival time of entanglement, on the other hand, with the increase of squeezed amplitude parameters, the robustness of quantum discord is more and more superior to concurrence and is more advantage to keep the system quantum correlations. The further study results show that the increase of the initial relative phase of coupling superconducting qubits can also keep the quantum correlations.     

依赖强度耦合双模Jaynes-Cummings 模型的纠缠和场熵演化

应用von Neumann熵研究了依赖强度耦合双模Jaynes-Cummings模型中原子与光场的纠缠度。给出了两模初始场均处于相干态和双模压缩真空态两种情况下熵演化的数值结果。讨论了初始场强度对原子―场纠缠度的影响。发现在强场条件下，原子与光场基本稳定在最大纠缠态但伴随着周期性的脉冲式解纠缠。     

Coherent Preservation of Two-Qubit Quantum Entanglement in the Strong Coupling Region

The entanglement of two qubits is investigated in the range of their ultra-strongly coupling with a quantum oscillator. The two qubits are initially in four Bell states and they are under the control mechanism of the coherent state of the quantum oscillator. There are four parameters: the average number of the coherent state, the ultra-strong coupling strength, the ratio of two frequencies of qubit and oscillator, and the inter-interaction coupling of the two qubits in the mechanism, and they all are influential parameters on the entanglement of the two qubits. One Bell state |0>is easyily kept and is trivial case. The novel results show that there is one state |I₀> among the other three Bell states which the entanglement of the two qubits could be almost completely preserved. The possibility is made into reality by the appropriate choice of the four influential parameters. We give two different schemes to choose the respective parameters to maintain the entanglment of |I₀> almost undiminished. The results will be useful for the quantum information process.     

Quantum discord dynamics of two qubits in single-mode cavities

The dynamics of quantum discord for two identical qubits in two independent single-mode cavities and a common single-mode cavity are discussed. For the initial Bell state with correlated spins, while the entanglement sudden death can occur, the quantum discord vanishes only at discrete moments in the independent cavities and never vanishes in the common cavity. Interestingly, quantum discord and entanglement show opposite behavior in the common cavity, unlike in the independent cavities. For the initial Bell state with anti-correlated spins, quantum discord and entanglement behave in the same way for both independent cavities and a common cavity. It is found that the detunings always stabilize the quantum discord.     

与压缩真空库耦合的单模腔内三量子点中激子纠缠

研究了与压缩真空库场耦合的单模腔中三个量子点中激子间纠缠的动力学行为.结果表明：如果不考虑腔模与激子吸收，激子演化为纯的纠缠态.当腔场与一压缩真空库耦合时，激子间形成混合三模高斯纠缠态；在长时极限下，激子态为一稳定的混合三模高斯纠缠态.通过求解激子的特征函数，发现激子态的纯度与纠缠不仅依赖于腔场的初态，并且还与库的双光子关联强度密切相关. 关键词： 纠缠 纯度 压缩真空库 量子点     

Robustness investigations on quantum entanglement and quantum discord of coupled qubits in squeezed vacuum reservoir

We investigate the quantum discord of coupled qubits in squeezed vacuum reservoir and compare it with the quantum entanglement of system. We find that the quantum discord and entanglement perform completely oppositely with the change of squeezed parameters. Quantum discord survives longer with the increase of squeezed amplitude parameter and entanglement death faster on the contrary. Under high squeezed amplitude parameter, the quantum discord can keep nonzero which indicate that the quantum discord is more robust than entanglement. We also find that the purity reduction of the initial quantum state will lead to the decay of concurrence or quantum discord. However, the quantum discord damps remarkably more slowly and survives longer than concurrence.     

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.     

Bell态原子与双模纠缠相干光场相互作用的纠缠特性

运用Negativity熵研究了Bell态原子与双模纠缠相干光场相互作用系统中两个全同二能级原子之间的纠缠演化特性.分析了光场强度、光场纠缠度及原子间相互作用强度对纠缠的影响.结果表明:原子处于|β11〉时,两原子始终处于最大纠缠态;原子处于|β00〉时,初始纠缠的两原子始终较长时间处于退纠缠状态;原子处在|β10〉时,增大双模光场的平均光子数可以明显增大两原子之间的纠缠度并保持较大的纠缠状态;原子初态处在|β01〉时,原子间的相互作用强度对双原子间纠缠度有较显著的非线性调制作用.     

Entanglement Between Two Dipole-Coupled Qubits Interacting with Two Independent Slightly Detuned Cavity Modes

Considering the generalized double Jaynes-Cummings model, we examine the entanglement between two non-identical dipole-dipole coupled qubits interacting with two independent detuned vacuum cavity modes. We calculate the negativity as a measure of qubits entanglement. We find that entanglement parameter evolve periodically with time and the period are affected by the model parameters and initial states of qubits. For unentangled initial states the detuning and dipole-dipole interaction affect only the period of entanglement oscillations, not the maximum value of entanglement. For entangled states the detuning stabilizes the entanglement parameter oscillations. According to choice of initial entangled state the dipole-dipole strength is greatly enhances or weakens the oscillations of the entanglement parameter.

     

Decoherence and protection of entanglement of a system of three qubits driven by a classical Gaussian distributed fluctuating field

We consider a system of three uncoupled entangled qubits undergoing a decoherence process (DP) induced by a classical environmental noise portrayed by a Gaussian distributed fluctuating field with either Ornstein–Uhlenbeck (OU) or Gaussian (G) autocorrelation function. The impacts of such a DP on the entanglement of the qubits are analyzed in detail when they are initialized either in the GHZ- or W-type states and interact with the fluctuating field in three different scenarios namely, common, independent and mixed environment(s). We found that: (i) the way the qubits interact with the noise as well as their initial state play an important role towards the protection of entanglement; (ii) there are optimal parameters which permit to delay or totally avoid the disentanglement of the qubits; (iii) irrespective of the qubit-noise coupling (QNC) scenario and the initial prepared state considered, the OU noise is more injurious to the survivorship of entanglement than the G one. Specifically, we show that, irrespective of the QNC scenario and the character of the noise considered, the DP disentangles the qubits more quickly when they are initialized in the W-type states than in the GHZ-type one. Furthermore, we show that when the initial state of the qubits is considered to be a W-type state, the disentanglement occurs more rapidly in the common environment (CE) scenario followed by the mixed environments (MEs) scenario than in the independent environments (IEs) one. However, the situation is completely reversed when a GHZ-type state is considered.     

Dynamics control of geometric quantum discord for two coupling qubits in a squeezed vacuum reservoir

We investigate the dynamics of geometric quantum discord of coupled qubits in a squeezed vacuum reservoir. The results show that there is distinct difference between the dynamics of geometric quantum discord and that of quantum entanglement near (or away from) the decoherence free subspace. We also find that the squeezed vacuum reservoir with high squeezed amplitude is more suitable for geometric quantum discord to survive. The robustness of geometric quantum discord is stronger than that of quantum entanglement.     

Environmental Effects on Two-Qubit Correlation in the Dispersive Jaynes-Cummings Model

Total, classical and quantum correlations as well as entanglement are studied for a two-qubit system, where each qubit is placed in a micro cavity described by the dispersive Jaynes-Cummings model. Not only the loss of cavity photons but also the effect of the qubit-photon interaction on the loss is taken into account. The two-qubit system is initially prepared in a Bell diagonal state with a single mixing parameter and the cavity photon is either in a superposition of vacuum and single-photon states or in a weak coherent state. It is shown that more correlation of the two qubits can survive as an initial value of the cavity photon number is smaller. There is a threshold value of the cavity photon number, below which the stationary state becomes inseparable. Furthermore it is found that the external environment which causes the cavity loss has two effects; one brings about the decay of the correlations and the other suppresses the decay.     

Quantum entanglement and nonlocality properties of two-mode Gaussian squeezed states

Quantum entanglement and nonlocality properties of a family of two-mode Gaussian pure states have been investigated. The results show that the entanglement of these states is determined by both the two-mode squeezing parameter and the difference of the two single-mode squeezing parameters. For the same two-mode squeezing parameter, these states show larger entanglement than the usual two-mode squeezed vacuum state. The violation of Bell inequality depends strongly on all the squeezing parameters of these states and disappears completely in the limit of large squeezing. In particular, these states can exhibit much stronger violation of local realism than two-mode squeezed vacuum state in the range of experimentally available squeezing values.     

Continuous-Variable Entanglement in a Coupled Field-Mesoscopic Josephson Junction System

Continuous-variable entanglement in the interacting system of a mesoscopic Josephson junction with a squeezed field is investigated. It is shown that when the cavity field is initially prepared in a squeezed vacuum state and the junction in its lowest energy state, the coupling system can evolve into a two-mode Caussian state. The timedependent characteristic function in the Wigner representation for the system is analytically obtained, and the squeezing degree of the initial cavity field turns out to have not only an apparent enhancing but also a weakening effect on the entanglement of the coupling system under suitable parameter conditions.     

Non-Markovian dynamics of two non-coupled qubits interacting with two separate reservoirs with different spectral densities

The dynamics of two non-coupled qubits independently interacting with their reservoirs is solved by the time convolutionless projection operator method. We study two-qubit quantum correlation dynamics for two different types of spectral densities, which are a Lorentzian distribution and an Ohmic spectral density with a Lorentzian-Drude cutoff function. For two qubits initially prepared in the initial Bell state, quantum discord can keep longer time and reach larger values in nonMarkovian reservoirs for the first spectral distribution or by reducing the cutoff frequency for the second case. For the initial Bell-like state, the dynamic behaviors of quantum discord and entanglement are compared. The results show that a long time of quantum correlation can be obtained by adjusting some parameters in experiment and further confirm that the discord can capture quantum correlation in addition to entanglement.