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arXiv:0912.4617 · Journal of Physics B Atomic Molecular and Optical Physics

Two atoms in dissipative cavities in dispersive limit: entanglement sudden death and long-lived entanglement

Jian-Song Zhang, Ai-Xi Chen, M Abdel-Aty

Published Dec 21, 2009• 37 citations
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Abstract

We investigate the entanglement dynamics and coherence of two two-level atoms interacting with two coherent fields of two spatially separated and dissipative cavities. It is in particular shown that entanglement sudden death is obtained within a short interaction time. However, after a long interaction time a long-lived entanglement is shown; that is, the initial entanglement of two atoms could be partially preserved. In addition, the coherence of the two atoms will not be lost during the evolution.

DOI
10.1088/0953-4075/43/2/025501

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We investigate the entanglement dynamics and coherence of two two-level atoms interacting with two coherent fields of two spatially separated and dissipative cavities. It is in particular shown that entanglement sudden death is obtained within a short interaction time. However, after a long interaction time a long-lived entanglement is shown; that is, the initial entanglement of two atoms could be partially preserved. In addition, the coherence of the two atoms will not be lost during the evolution.
The quantum dynamics of two entangled two-level atoms initially in extended Werner-like (EWL) states is studied. Each of the two atoms is located within an isolated and dissipative cavity. If the interaction time of atoms and cavities is not very long, the amount of quantum discord and entanglement between two atoms decreases as the system evolves. The sudden death of quantum discord and entanglement of two atoms occurs within a short interaction time. However, after a long interaction time, quantum discord and entanglement of two atoms could be partially preserved due to the long-lived nature of quantum discord and entanglement. Surprisingly, we find the amount of long-lived quantum discord could be smaller than that of long-lived entanglement. Thus, entanglement may be more robust than quantum discord against decoherence.
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 investigate the entanglement dynamics via the concurrence of two distant atoms interacting off-resonantly with two cavity fields in Fock states, respectively. We find that the evolution of entanglement has sudden death and sudden birth phenomena, that with the increase of photon numbers in the two cavities, the alternate frequency of sudden death and sudden birth turns fast, and that the amplitude of concurrence oscillates regularly with oscillation frequency becoming slow when the cavity fields have the same photon numbers. While, the maximum of concurrence declines and the amplitude of concurrence oscillates irregularly when the two cavity fields have different photon numbers. In addition, we find the length of death time is dependent on the initial entanglement.
The entanglement dynamics of two atoms initially in an entangled state system interacting with a bimodal field is investigated by making use of the concurrence and linear entropy.The effect of the initial entanglement degree of two atoms and the cavity field on the time evolution of concurrence is analyzed.The results show that the phenomenon of sudden death of the entanglement between two atoms occurs.The length of the death time interval is independent of the initial entanglement degree of two atoms.However,the death time depends on the initial entanglement degree of the cavity field.The atom and the field are entangled during all the evolution process.