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Communications in Theoretical Physics

Dynamic Behavior of Entanglement Between Two Spatially Separated Atoms in Two Dissipative and Driven Cavity Fields

Cui Hui-Ping, Jian Li, Liu Jin, Li Jun-Gang

Published Mar 1, 2009• 1 citation
Publisher

Abstract

We consider two two-level atoms, interacting with two independent dissipative cavities, each of which is driven by an external source. The two cavity fields are both initially prepared in the coherent states, and the two two-level atoms are initially prepared in the singlet state |Ψ − ⟩ = (|eg⟩ – |ge⟩)/√2. We investigate the influence of the damping constant κ, the intensity of the external sources F, and the relative difference of the atomic couplings r on the entanglement between the two atoms. In the dispersive approximation, we find that the entanglement between the two atoms decreases with the time evolution, and the decreasing rate of entanglement depends on the values of F/κ, κ/ω, and r. For the given small values of F/κ and κ/ω, on the one hand, the increasing of r favors entanglement decreasing of the atomic system, on the other hand, when r → 1 the entanglement decreasing becomes slower. With the increasing of the value of κ/ω, the influence of r on the decreasing rate of entanglement becomes smaller, and gradually disappears for the big value of κ/ω.

DOI
10.1088/0253-6102/51/3/26

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We consider two two-level atoms, interacting with two independent dissipative cavities, each of which is driven by an external source. The two cavity fields are both initially prepared in the coherent states, and the two two-level atoms are initially prepared in the singlet state |Ψ − ⟩ = (|eg⟩ – |ge⟩)/√2. We investigate the influence of the damping constant κ, the intensity of the external sources F, and the relative difference of the atomic couplings r on the entanglement between the two atoms. In the dispersive approximation, we find that the entanglement between the two atoms decreases with the time evolution, and the decreasing rate of entanglement depends on the values of F/κ, κ/ω, and r. For the given small values of F/κ and κ/ω, on the one hand, the increasing of r favors entanglement decreasing of the atomic system, on the other hand, when r → 1 the entanglement decreasing becomes slower. With the increasing of the value of κ/ω, the influence of r on the decreasing rate of entanglement becomes smaller, and gradually disappears for the big value of κ/ω.
We consider two two-level atoms, which are located in two independent dissipative cavities. The two atoms are initially prepared in the singlet state. We investigate the influence of dissipation on the entanglement between the two atoms. In the case of resonance the degree of the entanglement can fall abruptly to zero, which is the so-called sudden death of entanglement. It is noted that when two atoms are in a common environment, the singlet state is a decoherence-free state. When the dispersive limit is fulfilled, the degree of entanglement between the two atoms is oscillating at first, then it arrives at a steady value, which increases with the increase of the damping constant κ; when both fields are initially in the vacuum state, the entanglement between the two atoms will not decay.
= 被准备(| 例如 | ge )/√2。我们在在二个原子之间的纠纷上调查抑制经常的 κ ，外部来源 F 的紧张，和原子政变石楠 r 的相对差别的影响。在散近似，我们发现在二个原子之间的纠纷与时间进化减少，并且纠纷的减少的率取决于 F/κ ， κ/ω ，和 r 的价值。为 F/κ 和 κ/ω 的给定的小值，在一方面，增加 r 赞成在另一方面，原子系统减少的纠纷什么时候 r → 1 减少的纠纷变得更慢。与增加 κ/ω 的价值，纠纷的 r on the decreasing 率的影响变得更小，并且逐渐地为 κ/ω 的大价值消失。
We investigate the influence of dissipation on the entanglement among N identical two-level atoms. We analyse the situation of N two-level atoms in a dispersive cavity or in N dispersive cavities, both in W-like and in GHZ states for N atoms. By considering the Jaynes–Cummings model in the dispersive regime, and a master equation formalism, we compute the time evolution of the entanglement of the atoms, in a variety of situations. We find that, depending on whether the atoms are located in one or N cavities, and on their initial entangled state, the subsequent dynamics will be very different, specifically, exponential decay to coherent oscillations, exponential decay to steady values, or collapse and revival.
We have investigated the entangleable properties of two two-level atoms inside the dissipative cavity coupled to a single-mode radiation field under the big detuning,and discussed the influence of the initial state of the two atoms,the cavitity decay constant and the mean photon number on the entanglement degree.It have shown that if the two atoms are initially in the exicited or the ground states,they will be separate always;if the two atoms are initially in the coherent superposition of the excited and the ground states,the influence of cavity dissipation on the entanglement degree will vanish gradually with the time evolution,but the dipole-dipole interaction can enhance the entanglement degree.
We give a fully analytical description of the dynamics of an atom dispersively coupled to a field mode in a dissipative environment fed by an external source. The competition between the unitary atom field (which leads to entanglement) and the dissipative field-environment couplings are investigated in detail. We find the time evolution of the global atom-field system for any intial state and we show that the atom-field steady state is, at most, classically correlated. For a chosen initial state, we evaluate the purity loss of the global system and of atomic and field subsystems as a function of time. We find that the source will tend to compensate for the dissipation of the field intensity and to accelerate decoherence of the global and atomic states. A result pertinent to quantum information is the quantification of concurrence during the dissipative dynamics. An analytical expression for the time evolution of the concurrence is given.
We present the time evolution of a two-level atom interacting dispersively with an electromagnetic field in a dissipative cavity. We investigate the influence of dissipation on the entanglement of the two subsystems (atom+field).(\mathrm{atom}+\mathrm{field}).(atom+field). Simple but realistic, the model displays several nontrivial quantum features, which emerge when an environment is taken into account: the cavity is shown to have practically no influence in the coherence properties of the field from the qualitative point of view. On the other hand, although the atom is not directly coupled to the cavity modes, its coherent properties are strongly influenced by dissipation both qualitatively as well as quantitatively.