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Journal of Experimental and Theoretical Physics

Decoherence and entanglement in radiative decay of a diatomic system

Ashat M. Basharov

Published Jun 1, 2002• 49 citations
Publisher

Abstract

It is shown that, in the Markov approximation, relaxation of two noninteracting atoms in the field of a common thermostat leads not only to decoherence but also to the opposite process of the entanglement of atomic states, which can take on a stationary value depending on the initial conditions. This region of initial conditions narrows as the mean number of photons in the thermostat increases. The main radiative mechanism destroying an arbitrary initial entanglement of atoms is interaction of each atom with its own thermostat independent of the other. All Markov relaxation models under consideration are based on the Lindblad equations.

DOI
10.1134/1.1493157

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It is shown that, in the Markov approximation, relaxation of two noninteracting atoms in the field of a common thermostat leads not only to decoherence but also to the opposite process of the entanglement of atomic states, which can take on a stationary value depending on the initial conditions. This region of initial conditions narrows as the mean number of photons in the thermostat increases. The main radiative mechanism destroying an arbitrary initial entanglement of atoms is interaction of each atom with its own thermostat independent of the other. All Markov relaxation models under consideration are based on the Lindblad equations.
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.
We investigate system-environment correlations based on the exact dynamics of a qubit and its environment in the framework of pure decoherence (phase damping). We focus on the relation of decoherence and the buildup of system-reservoir entanglement for an arbitrary (possibly mixed) initial qubit state. In the commonly employed regime where the qubit dynamics can be described by a Markov master equation of the Lindblad type, we find that for almost all qubit initial states inside the Bloch sphere, decoherence is complete while the total state is still separable---no entanglement is involved. In general, both ``separable'' and ``entangling'' decoherence occurs, depending on the temperature and initial qubit state. Moreover, we find situations where classical and quantum correlations periodically alternate as a function of time in the regime of low temperatures.
In the consideration of Milburn model of intrinsic decoherence,we investigate the entanglement between two two-level atoms interacting with a Fock state of single-mode quantized radiation field.The reduced density matrix of the atom system is given explicitly.Due to the intrinsic decoherence,the entanglement of the atoms will decrease as the evolution of the system.And finally,the atoms system will approach a stationary state which the stationary entanglement depends on the initial states of the field and the atoms.Here,the entanglement is calculated by making use of the concurrence.
Time evolution of a quantum system which is influenced by a stochastically fluctuating environment is studied by means of the stochastic Liouville equation. The two different types of the stochastic Liouville equation and their relation are discussed. The stochastic Liouville equation is shown to be derived from the quantum master equation of the Lindblad under certain conditions. Relaxation processes of single and bipartite quantum systems which are initially correlated with a stochastic environment are investigated. It is shown the possibility that the stochastic fluctuation can create coherence and entanglement of a quantum system with the assistance of the initial correlation. The results are examined in the pure dephasing processes of qubits, which are caused by the nonstationary Gauss-Markov process and two-state jump Markov process.