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Journal of Physics Conference Series

Entanglement recovered periodically

Luis Roa, R. Pozo-González, Marius Schaefer, P. Utreras-SM

Published Nov 1, 2008• 0 citations
Publisher

Abstract

We study the entanglement dynamics of two not interacting atoms coupled weak and far from the resonance with the same single mode of the field.We consider two special initial states of the atoms.Specifically we study the cases when the atoms start in a pure entangled state and in a mixed state.When the field mode is initially in a coherent or thermal state, we find that in general in the high energy limit there is no entanglement between the two atoms, however at well defined moments the initial entanglement is as suddenly recovered as removed.

DOI
10.1088/1742-6596/134/1/012002

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We study the entanglement dynamics of two not interacting atoms coupled weak and far from the resonance with the same single mode of the field.We consider two special initial states of the atoms.Specifically we study the cases when the atoms start in a pure entangled state and in a mixed state.When the field mode is initially in a coherent or thermal state, we find that in general in the high energy limit there is no entanglement between the two atoms, however at well defined moments the initial entanglement is as suddenly recovered as removed.
We study how the entanglement between two atoms can be created or modified even when they do not interact but when each of them interacts dispersively, i.e., weak and far from the resonance with a single mode of the field. Considering that regime we apply a method which makes use of a small nonlinear deformation of the usual SU(2) algebra in order to obtain the effective Hamiltonian describing correctly the dynamics for any initial states. In particular we study two cases: In the first one we consider each atom initially in a pure state and in the second case we assume that they start in a Werner state. We find that both atoms can reach, periodically, maximum entanglement if each of them starts in any eigenstate of the x-componet of the Pauli oprator, independent of the initial Fock state of the mode. Thus we find that a dispersive vacuum can generate entanglement between two two-level atoms. In the second case and when the field mode is initially in a coherent or thermal state, we find that in the high energy limit, in general, there is no entanglement between the two atoms however at well defined moments the initial entanglement is as suddenly recovered as removed. This time behavior looks like narrow beats separated by the so called entanglement dead valleys.
We study how the entanglement between two atoms can be created or modified even when they do not interact but when each of them interacts dispersively, i.e., weak and far from the resonance, with a single mode of the field. In particular, we study two cases: First we consider each atom to be initially in a pure state and secondly we assume that they start in a Werner state. Analytically we find that both atoms can, periodically, reach maximum entanglement if each of them starts in any state belonging to the Bloch sphere equator, independent of the initial Fock state of the mode. Thus, in particular, we find that a dispersive vacuum mode can generate entanglement between two two-level atoms. In the second case, when the field mode is initially in a coherent or thermal state we find that, in the high energy limit, in general there is no entanglement between the two atoms. However, at well defined moments, the initial entanglement appears and disappears suddenly, becoming a narrow entanglement-beats structure.
We analyze the time evolution of quantum entanglement in a model consisting of two two-level atoms interacting with a two-mode electromagnetic field for a variety of initial states and interatomic separations. We study two specific atomic separations which give rise to symmetric atom-field couplings. For general atomic distances we consider a subset of initial states analytically, and then treat the more general situation numerically. We examine a variety of qualitative features such as entanglement sudden death, dynamical generation, protection, and transfer between subsystems. Our analysis shows a stark contrast in features of entanglement between the two special coupling schemes often considered; further, these features are uncharacteristic of those arising for general distances, due to the high degree of symmetry present in the special cases. The variety of behaviors in these two-mode cases suggest the importance of considering atomic separation carefully for any model where two atoms interact with a common field.
We examine the dynamics of bipartite quantum entanglement between a two-level atom and the electromagnetic field. We begin with the Jaynes-Cummings model with a single field mode and examine in detail the exact time evolution of entanglement, including cases where the atomic state is initially mixed and the atomic transition is detuned from resonance. We then explore the effects of other nearby modes by calculating the exact time evolution of entanglement in more complex systems with two, three, and five field modes. For these cases we can obtain exact solutions which include the strong-coupling regime. Finally, we consider the entanglement of a two-level atom with the infinite collection of modes present in the intracavity field of a Fabre-Perot cavity. In contrast to the usual treatment of atom-field interactions with a continuum of modes using the Born-Markov approximation, our treatment in all cases describes the full non-Markovian dynamics of the atomic subsystem under general couplings. Only when an analytic expression for the infinite mode case is desired do we need to make a weak coupling assumption which at late times approximates Markovian dynamics.
In this paper, we have investigated the entanglement between two dipole coupled two-level atoms. The model, in which only one atom is trapped in an lossless cavity and interacts with single-mode thermal field, and the other one can be spatially moved freely outside the cavity has been carried out. We have considered the effect of the atomic coherence on the entanglement behavior. We have shown that a thermal field might cause high entanglement between the atoms both for coherent and incoherent initial atomic states only for small values of the cavity mean photon number. In the considered model the atoms would get entangled even when both atoms are initially in the excited state. We have also derived that the degree of entanglement is weakly dependent on the strength of dipole-dipole interaction for coherent initial states.