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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum correlations in the system of two two-level atoms

Ashat M. Basharov, A. A. Bashkeev

Published Apr 20, 2004• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.562221

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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.
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.
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.
In this paper, we consider the entanglement dynamics of two identical qubits (two-level atoms) accompanied by dipole–dipole interaction within a common reservoir in the strong and weak coupling regimes. We suppose that the qubits move in the reservoir which is at zero temperature. Using the time-dependent Schrödinger equation, the state vector of the qubits-reservoir system is obtained by which we can evaluate the concurrence as a suitable measure of entanglement between the two qubits. The results show that by choosing special initial conditions for the qubits, a different dynamical behavior of entanglement is visible in such a way that entanglement protection occurs. Also, we find that the qubit motion in the absence of dipole–dipole interaction leads to preservation or at least more slowly decay of entanglement. However, in the presence of dipole–dipole interaction with the movement of qubits, different results can be observed which depend on the initial states of the qubits, i.e. entanglement may or may not be protected.
By exactly solving the model of two two-level atoms with dipole-dipole interaction, interacting with a common environment, quantum entanglement and quantum discord of two atoms are obtained. In this paper, the influences of the non-Markovian effect of environment, the dipole-dipole interaction of two atoms and the detunings of the central frequency of the cavity and the transition frequency of the atoms on quantum entanglement and quantum discord dynamics of two atoms are comprehensively considered. The study shows that in the non-Markovian regime and the resonant case, if two atoms are initially in the entangled state, the damping of quantum entanglement and quantum discord will be remarkably suppressed. More specially, in the off-resonant case, the disentanglement time of the two atoms can be considerably prolonged. On the other hand, if two atoms are initially in the separable state, the dipole-dipole interaction can enhance the amplitude of oscillations of quantum entanglement and quantum discord in a short time, but the steady values of quantum entanglement and quantum discord cannot be changed by the dipole-dipole interaction in the long-time limit. Finally, the different influences of the dipole-dipole interaction on quantum entanglement and quantum discord also are discussed.
In this paper we study the quantum entanglement of two identical qubits which interact with electromagnetic field and each other by time-dependent dipole-dipole interaction. We develop original method in path integral approach for numerical calculation of density matrix and Peres-Horodecki parameter (the measure of qubits entanglement). By the use of obtained equations we investigate the dependence of quantum entanglement on dipole-dipole interaction amplitude and frequency as well as qubits phase difference. The results indicate on possibility of high-entanglement states exiting and long-time non-destructive control of them.