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Applied Mathematics

Entanglement and Quantum Discord of Two Moving Atoms

Nour Zidan

Published Jan 1, 2014• 8 citations
Publisher

Abstract

In this paper we discuss two measures for the quantumness of correlations (quantum discord and entanglement) of two isolated moving atoms which are initially in Werner state. We compare and analyze the effect of the atomic motion in quantum discord and entanglement. The results show that the atomic motion related to the field mode structure parameter can make the entanglement and quantum discord evolve periodically. The results also indicate that the entanglement suddenly disappears during the evaluation but quantum discord remains non zero, so quantum discord is considered as indicator of disentanglement.

DOI
10.4236/am.2014.516240

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In this paper we discuss two measures for the quantumness of correlations (quantum discord and entanglement) of two isolated moving atoms which are initially in Werner state. We compare and analyze the effect of the atomic motion in quantum discord and entanglement. The results show that the atomic motion related to the field mode structure parameter can make the entanglement and quantum discord evolve periodically. The results also indicate that the entanglement suddenly disappears during the evaluation but quantum discord remains non zero, so quantum discord is considered as indicator of disentanglement.
Abstract Considering a double JC model, this paper investigates the quantum discord dynamics of two isolated moving two-level atoms each interacting with a single-mode thermal cavity field, and studies the effect of the atomic motion and the field-mode structure on quantumdiscord. The results show that, on the one hand the quantum discord evolves periodically with time and the periods are affected by the atomic motion and the field-mode structure; on the other hand, the quantum discord still can capture the quantum correlation between the two atoms when the entanglement is zero. It is interesting to note that the quantum discord can be effectively preserved by controlling the field-mode structure parameter
Considering a double J-C model with intensity-dependent coupling, we have studied the effects of the intensity-dependent coupling, the mean photon numbers and the atomic motion, on the entanglement and quantum discord between the two two-level atoms when the moving atoms are initially in a maximally entangled state and the fields are in the single-mode thermal fields. The results show that, the entanglement and quantum discord disappear and revive periodically, and can have up to their starting values after revival. A rise in cavity temperature accelerates the death of the entanglement and quantum discord. In addition, the field-mode structural parameter has a strong effect on the entanglement and quantum discord in the system. When the field-mode structural parameter takes a suitable value, the entanglement and quantum discord of the two atoms can be kept from start to finish.
The quantum dynamics of two entangled two-level atoms initially in extended Werner-like (EWL) states is studied. Each of the two atoms is located within an isolated and dissipative cavity. If the interaction time of atoms and cavities is not very long, the amount of quantum discord and entanglement between two atoms decreases as the system evolves. The sudden death of quantum discord and entanglement of two atoms occurs within a short interaction time. However, after a long interaction time, quantum discord and entanglement of two atoms could be partially preserved due to the long-lived nature of quantum discord and entanglement. Surprisingly, we find the amount of long-lived quantum discord could be smaller than that of long-lived entanglement. Thus, entanglement may be more robust than quantum discord against decoherence.
We study the non-Markovian effect on the dynamics of the quantum discord by exactly solving a model consisting of two independent qubits subject to two zero-temperature non-Markovian reservoirs, respectively. Considering the two qubits initially prepared in Bell-like or extended Werner-like states, we show that there is no occurrence of the sudden death, but only instantaneous disappearance of the quantum discord at some time points, in comparison to the entanglement sudden death in the same range of the parameters of interest. This implies that the quantum discord is more useful than the entanglement to describe the quantum correlation involved in quantum systems.
Herein, we present an approach to look for the best phenomenon to measure quantum correlation. The system of two isolated qubits each interacting with a single-mode cavity was theoretically created to study the quantum correlation. Some of the phenomena, such as the quantum discord and concurrence, were generated through such a system. The influences of initial state purity, qubit motion, and detuning parameters were discussed for the phenomena. These parameters for a specific value show that the behavior of phenomena are analogous. It is interesting to mention that some values of detuning undergo a sudden death of phenomena, and the quantum discord still captures the qubits quantum correlation. We predict that the quantum discord may be a better measure of quantum correlation than concurrence.
We study the dynamics of classical correlation and quantum discord of two coupled two-level atoms interacting with a cavity initially in vacuum, coherent and thermal equilibrium states, respectively. The interplay between the atom–atom coupling and mean number of photons is considered. We find that, for a cavity in a vacuum state, classical correlation or quantum discord shows a sudden change in behaviour during the evolution, and evolves periodically for zero and very large qubit–qubit couplings. However, for coherent and thermal equilibrium states, the classical correlation and quantum discord present the phenomenon of collapse–revival when the qubit–qubit coupling is much greater than the mean number of photons. The period of collapse–revival becomes long as the qubit–qubit coupling and mean number of photons increase. The relationship between quantum discord and entanglement in the studied system is considered.