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arXiv:1011.5114 · Chinese Physics Letters

Non-Markovian Dynamics of Quantum and Classical Correlations in the Presence of System-Bath Coherence

Chuan‐Feng Li, Hao-Tian Wang, Hong-Yuan Yuan, Rong-Chun Ge, Guang‐Can Guo

Published Dec 1, 2011• 7 citations
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Abstract

We present a detailed study on the dynamics of two-qubit correlations in non-Markovian environments, applying the hierarchy equations approach. This treatment is free from the limitation of perturbative, Markovian or rotating wave approximations. It is shown that crossovers and sudden changes in the classical and quantum correlations can appear when the strength of the interaction between qubits is gradually reduced. For some special initial states, there are even sudden transitions between the classical and quantum correlations.

DOI
10.1088/0256-307x/28/12/120302

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We present a detailed study on the dynamics of two-qubit correlations in non-Markovian environments, applying the hierarchy equations approach. This treatment is free from the limitation of perturbative, Markovian or rotating wave approximations. It is shown that crossovers and sudden changes in the classical and quantum correlations can appear when the strength of the interaction between qubits is gradually reduced. For some special initial states, there are even sudden transitions between the classical and quantum correlations.
We study bipartite and multipartite correlations of several coupled qubits within a common non-Markovian bath using the hierarchy equation method. This method does not use the rotating-wave and Born–Markovian approximations. The interaction between the qubits and their coupling strength with the bath have remarkable influence on the dynamics of quantum correlations. The entanglement sudden death (ESD) phenomenon, the amount of stationary state concurrence and spin squeezing can be controled by the non-Markovianity of the environment and interactions between qubits. These properties may be useful for purposes of quantum information processing with multiqubit system in non-Markovian environments.
We investigate quantum synchronization and correlations of two qutrits in one non-Markovian environment using the hierarchy equation method. There is no direct interaction between two qutrits and each qutrit interacts with the same non-Markovian environment. The influence of the temperature of the bath, correlation time and coupling strength between qutrits and bath on the quantum synchronization and correlations of two qutrits are studied without the Markovian, Born and rotating wave approximations. We also discuss the influence of dissipation and dephasing on the synchronization of two qutrits. In the presence of dissipation, the phase locking between two qutrits without any direct interaction can be achieved when each qutrit interacts with the common bath. Two qutrits within one common bath cannot be syncrhonized in the purely dephasing case. In addition, the Arnold tongue can be significantly broadened by decreasing the correlation time of two qutrits and bath. Markovian baths are more suitable for synchronizing qutrits than non-Markovian baths.
"We investigate the dynamics of quantum correlation of two qubits under local dephasing channels. We demonstrate the constancy of quantum correlation for long interval of times despite the detrimental effects of the environments. The natural protection of quantum correlation is accompanied by losses of classical correlation. At a sharp time, quantum and classical correlations exchange their roles: quantum corre- lation starts to decay while classical correlations become constant. We have called this phenomenon “sudden transition between classical and quantum decoherence” [Physical Review Letters 104, 200401 (2010)] . Such a dynamical feature is not the result of the Markovian approximation, but it appears in a much richer way also in the non-Markovian scenario."
Abstract We investigate the freezing and sudden transition in the dynamical behavior of quantum and classical correlations in a system composed of two identical non-interacting qubits locally subjected to their own non-equilibrium environments. In contrast to the equilibrium case, one can observe striking results when a bipartite quantum system couples with the non-equilibrium dephasing environment with non-stationary and non-Markovian features. Remarkably, the finite time interval in which the quantum correlation remains impervious to decoherence can be further prolonged as the environment deviates from equilibrium. This reveals that the non-equilibrium parameter provides an alternative tool to efficiently control the appearance of a sudden transition in the decay rates of correlations and their immunity towards the decoherence. Furthermore, for certain initial states, the appearance of another time-interval over which quantum correlation remains constant and the revival of classical correlation not only depends on the non-Markovianity but also on the non-equilibrium parameter.
In this Thesis I discuss the exact dynamics of simple non-Markovian systems. I focus on fundamental questions at the core of non-Markovian theory and investigate the dynamics of quantum correlations under non-Markovian decoherence. \n \nIn the first context I present the connection between two different non-Markovian approaches, and compare two distinct definitions of non-Markovianity. The general aim is to characterize in exemplary cases which part of the environment is responsible for the feedback of information typical of non- Markovian dynamics. I also show how such a feedback of information is not always described by certain types of master equations commonly used to tackle non-Markovian dynamics. \n \nIn the second context I characterize the dynamics of two qubits in a common non-Markovian reservoir, and introduce a new dynamical effect in a wellknown model, i.e., two qubits under depolarizing channels. In the first model the exact solution of the dynamics is found, and the entanglement behavior is extensively studied. The non-Markovianity of the reservoir and reservoirmediated-interaction between the qubits cause non-trivial dynamical features. \n \nThe dynamical interplay between different types of correlations is also investigated. In the second model the study of quantum and classical correlations demonstrates the existence of a new effect: the sudden transition between classical and quantum decoherence. This phenomenon involves the complete preservation of the initial quantum correlations for long intervals of time of the order of the relaxation time of the system.
Dynamics of the quantum entanglement and quantum discord of two qubits in two independent baths and a common bath with the Lorentzian spectrum are studied exactly in the numerical sense within the hierarchy approach. The effects of the counter-rotating-wave terms from the system–bath coherence on these quantum correlations are systematically discussed and comparisons with previous ones under the rotating-wave approximation are also performed. For two independent baths, beyond the weak system–bath coupling, the counter-rotating-wave terms essentially change evolutions of both the entanglement and quantum discord. With increase of the coupling, revival of the entanglement after a period of complete disentanglement is suppressed dramatically and finally disappears, and the quantum discord becomes smaller monotonically. For the common bath, the entanglement is also suppressed by the counter-rotating-wave terms, but the quantum discord shows quite different behaviors if initiated from spin-correlated states. In the non-Markovian regime, the quantum discord is almost not influenced by the counter-rotating-wave terms and is generally finite in the long-time evolution at arbitrary coupling while in the Markovian regime, it is significantly enhanced with the strong coupling.