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Optics and Spectroscopy

Entanglement of atoms by a resonance classical electromagnetic field

Ashat M. Basharov, Ekaterina V. Moreva, Edward A. Manykin

Published Jun 8, 2004• 0 citations
Publisher

Abstract

It is shown that the interaction of a system of two two-level atoms with a resonance classical electromagnetic field under conditions of collective relaxation gives rise to quantum correlations and controlled entanglement. Various models of the bath are examined, such as the unidirectional, one-dimensional, and three-dimensional models, as well as a squeezed bath. As a measure of the entanglement, the minimum negative eigenvalue of the Peres-Horodecki matrix is used.

DOI
10.1134/1.1753627

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It is shown that the interaction of a system of two two-level atoms with a resonance classical electromagnetic field under conditions of collective relaxation gives rise to quantum correlations and controlled entanglement. Various models of the bath are examined, such as the unidirectional, one-dimensional, and three-dimensional models, as well as a squeezed bath. As a measure of the entanglement, the minimum negative eigenvalue of the Peres-Horodecki matrix is used.
A new mechanism of development of quantum correlations due to the combined effects of a common heat bath and a resonant classical electromagnetic field is analyzed for a system of two two-level atoms coupled by dipole-dipole interaction. Conditions are found under which arbitrary steady-state entanglement can be created in the absence of measurement in an entangled basis. The analysis of dynamics of entanglement is focused on the effects of dipole-dipole interaction, mean number of thermal photons, degree of squeezing of thermal radiation, classical field strength, and presence of additional decay channels.
The dynamics of appearance of a steady entangled state in an ensemble of two collectively decaying two-level atoms is studied on the basis of the Peres-Horodecki criterion with regard to the dipole-dipole interaction between the atoms and their frequency detuning. It is ascertained that, in the absence of dipole-dipole interaction, the steady-state entanglement is in many respects due to the coincidence of the frequencies of transitions in the atoms, whereas a difference in the frequencies, related to different positions of the atoms in a crystal or their thermal motion, destroys the steady-state entanglement. Upon a dipole-dipole interaction, a steady-state entanglement also exists and, in this case, depends strongly on the relationship between the magnitude of the dipole-dipole interaction, the constant of coupling with a thermostat, and the phase of the resonance wave; the entanglement appears only when the thermostat coupling constant is dominant.
Relying on the Peres-Horodecki criterion, we investigated the dynamics of appearance of the stationary entanglement in the system of two two-level atoms decaying in the field of common thermostat. We took into account their dipole-dipole interaction and the difference between their atomic frequencies. It was established, that in the absence of the dipole-dipole interaction the presence of the stationary entanglement has a strong dependence on the identity of atomic frequencies. The difference between them (due to their different locations in the crystal or thermal movement), leads to a disappearance of the stationary entanglement. Also we found the dependence of existence of the stationary entanglement from a correlation between the constant of the dipole-dipole interaction, the resonance wave shift and the constant of interaction with the thermostat field - it comes into existence only when the latter value becomes greater than the former ones.
In this paper the entanglement dynamics for system of two two-level atoms interacting with a mode of thermal electromagnetic field in lossless cavity has been investigated. Initial atomic states are the entangled Bell type states. Using the full set of eigenvectors of the Hamiltonian of the considered model we have derived the exact solution for the density matrix for the whole system. On its basis the reduced atomic density matrix and Peres - Horodetcki parameter have been calculated. Calculating of entanglement parameter shows the possibility of high degree of entanglement even for large intensity of thermal field. Thus there is a possibility of maintenance and control over the degree of entanglement.