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arXiv:1105.4041 · Physical Review A

Sudden transition between classical and quantum decoherence in dissipative cavity QED and stationary quantum discord

Qi-Liang He, Jing‐Bo Xu, Dao‐Xin Yao, Ye-Qi Zhang

Published Aug 8, 2011• 38 citations
arXivHTMLPDF

Abstract

We investigate the phenomenon of sudden transition between classical and quantum decoherence in the study of quantum discord for a dissipative cavity QED system, which consists of two noninteracting two-level atoms, each trapped in a dissipative cavity. It is found that the quantum discord between the two atoms, which are prepared initially in the X-type quantum states, is not destroyed by the dissipation of the cavities for a finite time interval, and the stationary quantum discord can arise in the interaction of atoms with cavities as the time approaches infinity. The transition time is sensitive to the initial state parameter of the two atoms and the mean photon number of the coherent field. Interestingly, the quantum discord between the two atoms is completely unaffected by the dissipation of the cavities if we choose the suitable value of the ratio, which depends on the decay rate of the two cavities and the atom-field coupling constant.

DOI
10.1103/physreva.84.022312

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We investigate the phenomenon of sudden transition between classical and quantum decoherence in the study of quantum discord for a dissipative cavity QED system, which consists of two noninteracting two-level atoms, each trapped in a dissipative cavity. It is found that the quantum discord between the two atoms, which are prepared initially in the X-type quantum states, is not destroyed by the dissipation of the cavities for a finite time interval, and the stationary quantum discord can arise in the interaction of atoms with cavities as the time approaches infinity. The transition time is sensitive to the initial state parameter of the two atoms and the mean photon number of the coherent field. Interestingly, the quantum discord between the two atoms is completely unaffected by the dissipation of the cavities if we choose the suitable value of the ratio, which depends on the decay rate of the two cavities and the atom-field coupling constant.
The dynamics of classical correlation and quantum correlation of two qubits in an independent and common dissipative cavity are studied. We show that for an independent case, the quantum correlation keeps constant and the correlation relation decays before the critical time point Ωt¯. On the other hand t>Ωt¯, for the classical correlation does not change and the quantum correlation is lost. These situations demonstrate that the phenomenon of sudden transition between classical and quantum decoherence appears during the time evolution. For the common case, the quantum correlation dynamics is quite different. It is displayed that for some initial states, the quantum correlation can increase up to the critical point of time, after which it decreases, which means that the quantum correlation presents a sudden change of behavior in their decay rates. But for other initial states, the quantum correlation can keep increasing up to some-steady state value. Furthermore, we also investigate the nonzero quantum correlation between two qubits induced by the dissipation of the cavity.
We investigate analytically the dynamics of classical and quantum correlations between two strongly driven atoms, each of which is trapped inside a dissipative cavity. It is found that there exists a finite time interval during which the quantum discord initially prepared in the X -type states is not destroyed by the decay of the cavities. The sudden transition between classical correlation and quantum discord is sensitive to the initial-state parameter, the cavity decay rate, and the cavity mode-driving field detuning. Interestingly, we show that the transition time can be prolonged significantly by increasing the degree of the detuning.
We investigate the dynamics of geometric quantum correlations for certain decoherence channels and discuss the necessary conditions for the existence of frozen geometric discord. As illustrative examples, we study the phenomenon of double sudden transitions in geometric discord for a system consisting of two noninteracting atoms inserted in two independent dissipative cavities and how the initial state parameters and decay rate of dissipative cavities affect the frozen time during which the geometric discord remains constant. We also explore the dynamics of geometric discord between two noninteracting atoms trapped in a common dissipative cavity and find that the geometric discord exhibits sudden transition between classical and quantum decoherence. Moreover, a nonzero stationary geometric discord can arise in both the independent cavity case and common cavity case.
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.
We investigate the quantum-to-classical crossover of a dissipative cavity field by measuring the correlations between two noninteracting atoms coupled to the cavity mode. First, we note that there is a time window in which the mode shows a classical behavior, which depends on the cavity decay rate, the atom-field coupling strength, and the number of atoms. Then, considering the steady state of two atoms inside the cavity, we note that the entanglement between the atoms disappears while the mean number of photons of the cavity field (n) rises. However, the quantum discord reaches an asymptotic nonzero value even in the limit of n→∞, whether n is increased coherently or incoherently. Therefore, the cavity mode always preserves some quantum characteristics in the macroscopic limit, which is revealed by the quantum discord.
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.