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arXiv:quant-ph/0612079

Narrow entanglement beats

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

Published Dec 11, 2006• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.quant-ph/0612079

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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 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 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.
Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.