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Journal of Physics B Atomic Molecular and Optical Physics

Influence of dissipation on the entanglement ofNtwo-level atoms located in one cavity orNcavities

Lin Li, Jian Zou, Jungang Li, Hui-Ping Cui, Bin Shao

Published Apr 7, 2008• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0953-4075/41/8/085507

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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 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.
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.
Decoherence of the dispersive Jaynes–Cummings model which is placed in a lossy cavity is studied by means of the time-convolutionless non-Markovian quantum master equation. The effect of the interaction between a two-level atom and photon field on the damping operator of the quantum master equation is made clear by calculating the decay of coherence and entanglement of the relevant system. It is shown that although the interaction effect on the damping operator is small when the cavity loss has the Markovian property, it becomes significantly large when the cavity loss is subject to the non-Markovian process. Furthermore, the quantum channel of the two-level atom derived by the dispersive Jaynes–Cummings model is investigated. The decay of entanglement of the two two-level atoms is examined to show the importance of the interaction effect on the damping operator.
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.
In this paper we consider the situation that three identical two-level atoms resonantly interact with three distant single-mode optical cavities via a one-photon hopping separately.Three atoms are in like-GHz state and therr optical cavities are all in vacuum state initially.Using the Jaynes-Cummings,the time evolution of the system is given.We adopt the entanglement tensor approach to quantify the degree of entanglement.The tripartite entanglement dynamics among three atoms and the entanglement dynamics between two atoms are studied.The influence of atomic states initially on tripartite entanglement among atoms and two-body entanglement between two atoms are discussed.The results obtained using the numerical method show:first,the time evolution of tripartite entanglement displays the periodic oscillation behavior and its oscillation period is not realted with the initial degree of entanglement among atmos;second the peak and mean of entanglement measures E3 and F2 incease with increasing of the initial degree of entanglement among atmos,which means that the larger the initial degree of entanglement among atoms,the layer the tripartite entanglement among atoms and the two-body entanglement between atoms;third,the phenomenon of sudden death of entanglement between two atoms occurs,and the length of the death time interval decreases with increasing of the initial degree of entanglement among atoms.This shows that the length of the death time interval of two-body entanglement can be decreased by selecting initially atomic state with high degree of entanglement among atoms.
We propose an experimental setup, feasible with present day technology, involving two highquality- factor cavities, one Ramsey zone and a two-level atom which interacts with them. The dynamics in the cavities is modeled by a dissipative dispersive Jaynes-Cummings model. Analytical expresions for the evolution superoperator in each part of the proposed setup and for the concurrence between the atom and the first cavity are given, and the pairwise entanglement of the subsystems is calculated numerically. We consider initial separable states given by the tensor product of a superposition of the two atomic relevant states and coherent states for the fields. We show that for realistic model parameters (including dissipation), when the dissipation rates are smaller than the dispersive frequencies (the ratio between the squared vacuum Rabi frequencies and the detunings), the final state of the cavity fields remains entangled.