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International Journal of Modern Physics B

The distribution of stationary correlations between qubits and the environment

Xiang-Ping Liao, Chang-Ning Pan, Rong Man-sheng, Mao-Fa Fang

Published Oct 10, 2019• 0 citations
Publisher

Abstract

We study the distribution of the stationary correlations in a system of two nonidentical as well as identical two-level atoms separated by an arbitrary distance and interacting with a squeezed vacuum. We investigate how the interatomic distance and the squeezing mean number of photons influence the way that one of the atoms is quantum correlated with the environment. Both for nonidentical and identical atoms, the approach of the two atoms can maximize the entanglement and quantum discord between the pair of atoms. For nonidentical atoms, the bigger the mean number of photons, the stronger the stationary correlations, i.e., entanglement of formation (EOF) and quantum discord (QD) between the qubit and the environment as the increase of distance. The increase of EOF and QD with the environment is always accompanied by a decrease of the correlations between the subsystems with regard to the interatomic distance no matter what the mean number of photons is. For identical atoms, the stationary correlations EOF and QD between each partition behave similarly with respect to the distance when the mean number of photons is very small.

DOI
10.1142/s0217979219502990

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We study the distribution of the stationary correlations in a system of two nonidentical as well as identical two-level atoms separated by an arbitrary distance and interacting with a squeezed vacuum. We investigate how the interatomic distance and the squeezing mean number of photons influence the way that one of the atoms is quantum correlated with the environment. Both for nonidentical and identical atoms, the approach of the two atoms can maximize the entanglement and quantum discord between the pair of atoms. For nonidentical atoms, the bigger the mean number of photons, the stronger the stationary correlations, i.e., entanglement of formation (EOF) and quantum discord (QD) between the qubit and the environment as the increase of distance. The increase of EOF and QD with the environment is always accompanied by a decrease of the correlations between the subsystems with regard to the interatomic distance no matter what the mean number of photons is. For identical atoms, the stationary correlations EOF and QD between each partition behave similarly with respect to the distance when the mean number of photons is very small.
The quantum correlations between a qubit and its environment are described quantitatively in terms of interatomic distance. Specifically, considering a realistic system of two two-level atoms and taking into account the dipole-dipole interaction and collective damping, the quantum entanglement and quantum discord are investigated during the dissipative process as functions of the interatomic distance. For atoms that are initially maximally entangled, it turns out that there is a critical distance at which each atom is maximally quantum correlated with its environment. Counterintuitively, the approach of the two atoms can maximize the entanglement between each one and the environment and, even at the same distance, minimize the loss of entanglement between the pair.
A system of two two-level atoms interacting with a squeezed vacuum field can exhibit stationary entanglement associated with nonclassical two-photon correlations characteristic of the squeezed vacuum field. The amount of entanglement present in the system is quantified by the well known measure of entanglement called concurrence. We find analytical formulas describing the concurrence for two identical and nonidentical atoms and show that it is possible to obtain a large degree of steady-state entanglement in the system. Necessary conditions for the entanglement are nonclassical two-photon correlations and nonzero collective decay. It is shown that nonidentical atoms are a better source of stationary entanglement than identical atoms. We discuss the optimal physical conditions for creating entanglement in the system, in particular, it is shown that there is an optimal and rather small value of the mean photon number required for creating entanglement.
In this paper, we have investigated the dynamics of the quantum correlation between two qubits of a system composed of an arbitrary number of qubits dissipating into a common environment. Our results imply that, when the initial state of the system contains one excitation, the quantum correlation of the quantum discord and the entanglement of formation can be generated between two qubits which have no interaction with each other but are interacting with a common environment. From our analysis, we find that the dynamics of the quantum discord and the entanglement of formation depends not only on the scaled time but also on the size of the system. The larger the size of the system is, the less the quantum discord and the entanglement of formation is generated. By using a comparison between the quantum discord and the entanglement of formation, we find that the quantum discord is more robust to the size of the system than the entanglement of formation is, in the sense that the former decreases more slowly with an increase of the size of the system than the latter does. In addition, the case of the initial state with two excitations is discussed.
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.
"or many years the entangled systems have been associated to the quantum world, while the separable systems with the classical world. Recently quantum discord showed that some separable states posses quantum correlation even when the entanglement is zero. In this work, we compare different features of quantum discord and entanglement of formation for two qubits in a common squeezed reservoir. We relate the quantum correlations with the “distance” of our initial condition from the decoherence free subspace where the system is not affected by environment. While for some initial conditions, the entanglement presents sudden death and revival, quantum discord does not. Still, is not clear the relation between these two measurements of “quantumness”."
In this paper, we investigate the quantum correlation of coupled qubits which are initially in maximally entangled mixed states in a squeezed vacuum reservoir. We compare and analyze the effects of squeezed parameters on quantum discord and quantum concurrence. The results show that in a squeezed vacuum reservoir, the quantum discord and quantum concurrence perform with completely opposite behaviors with the change of squeezed parameters. Quantum discord survives longer with the increase of squeezed amplitude parameter, but entanglement death is faster on the contrary. The results also indicate that the classical correlation of the system is smaller than quantum discord in a vacuum reservoir, while it is bigger than quantum discord in a squeezed vacuum reservoir. The quantum discord and classical correlation are more robust than quantum concurrence in the two reservoir environments, which indicates that the entanglement actually is easily affected by decoherence and quantum discord has a stronger ability to avoid decoherence in a squeezed vacuum reservoir.