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arXiv:0804.4869 · Physical Review A

Quantum dynamics in nonequilibrium environments

Clive Emary

Published Sep 8, 2008• 15 citations
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Abstract

We present a formalism for studying the behavior of quantum systems coupled to nonequilibrium environments exhibiting non-Gaussian fluctuations. We discuss the role of a qubit as a detector of the statistics of environmental fluctuations, as well as non-Markovian effects in both weak and strong-coupling limits. We also discuss the differences between the influences of classical and quantum environments. As examples of the application of this formalism we study the dephasing and relaxation of a charge qubit coupled to nonequilibrium electron transport through single and double quantum dots.

DOI
10.1103/physreva.78.032105

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We present a formalism for studying the behavior of quantum systems coupled to nonequilibrium environments exhibiting non-Gaussian fluctuations. We discuss the role of a qubit as a detector of the statistics of environmental fluctuations, as well as non-Markovian effects in both weak and strong-coupling limits. We also discuss the differences between the influences of classical and quantum environments. As examples of the application of this formalism we study the dephasing and relaxation of a charge qubit coupled to nonequilibrium electron transport through single and double quantum dots.
We theoretically study the non-Markovian dynamics of qubit systems coupled to nonequilibrium environments with nonstationary and non-Markovian statistical properties. The reduced density matrix of the single qubit system satisfies a closed third-order differential equation with all the higher-order environmental correlations taken into account and the reduced density matrix of the two qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for a given evolution time when the two qubit system is initially prepared in the composite Bell states and the extended Werner states, respectively. It is shown that the environmental nonstationary feature can suppress the decoherence and disentanglement dynamics and can reduce the coherence and entanglement revivals in non-Markovian dynamics regime. In addition, it is shown that the environmental non-Markovian feature can enhance the coherence revivals in the single decoherence dynamics and the entanglement revivals in the two qubit disentanglement dynamics, respectively. Furthermore, the environmental nonstationary and non-Markovian features can enhance the nonlocality of the two qubit system.
We study the open dynamics of a quantum two-level system coupled to an environment modeled by random matrices. Using the quantum channel formalism, we investigate different quantum Markovianity measures and criteria. A thorough analysis of the whole parameter space reveals a wide range of different regimes, ranging from strongly non-Markovian to Markovian dynamics. In contrast to analytical models, all non-Markovianity measures and criteria have to be applied to data with fluctuations and statistical uncertainties. We discuss the practical usefulness of the different approaches.
Nonequilibrium transport properties of quantum systems have recently become experimentally accessible in a number of platforms in so-called full-counting experiments that measure transient and steady-state nonequilibrium transport dynamics. We show that the effect of the measurement back-action can be exploited to establish general relationships between transport coefficients in the transient regime which take the form of fluctuation-dissipation theorems in the steady state. This result becomes most conspicuous in the transient dynamics of open quantum systems under strong-coupling to non-Markovian environments in nonequilibrium settings. In order to explore this regime, a new simulation method based in a hierarchy of equations of motion has been developed. We instantiate our proposal with the study of energetic conductance between two baths connected via a few level system.
We theoretically investigate the non-Markovian dynamical decoherence of a quantum system coupled to nonequilibrium environments with nonstationary statistical properties. We show the time evolution of the decoherence factor in real-imaginary space to study the environment-induced energy renormalization and backaction of coherence which are associated with the unitary and nonunitary parts of the quantum master equation, respectively. It is also shown that the nonequilibrium decoherence dynamics displays a transition between Markovian and non-Markovian and the transition boundary depends on the environmental parameters. The results are helpful for further understanding non-Markovian dynamics and coherence backaction on an open quantum system from environments.
We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.
We investigate the roles of different environmental models on quantum correlation decay behavior of a two-qubit composite system interacting with two independent environments. The most common environmental models (the single-Lorentzian model, the squared-Lorentzian model, the two-Lorentzian model and bandgap model) are analyzed. First, we note that, for the weak coupling regime, the monotonic decay speed of the quantum correlation is mainly determined by the spectral density functions of these different environments. Then, by considering the strong coupling regime we find that, contrary to what is stated in the weak coupling regime, the dynamics of quantum correlation primarily depends on the non-Markovianity of the environmental models.