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arXiv:quant-ph/0309114 · The European Physical Journal D

The non-Markovian quantum behavior of open systems

Heinz‐Peter Breuer

Published Apr 1, 2004• 27 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2004-00010-x

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We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the dynamical map describing the time evolution of physical states, and can be interpreted in terms of the information flow between the open system and its environment. The measure takes on nonzero values whenever there is a flow of information from the environment back to the open system, which is the key feature of non-Markovian dynamics.
The behavior of quantum coherence is studied under Markovian and non-Markovian dynamics for open quantum systems. For single qubit systems, we show that the coherence depending on the off-diagonal elements of the density matrix is the upper bound of the coherence depending on the relative entropy under both Markovian and non-Markovian processes. For two-qubit systems, in both Markovian and non-Markovian processes, quantum discord and coherence show less sensitivity to the initial state than quantum entanglement. We also find that the quantum discord has similar behaviors with coherence under both Markovian and non-Markovian dynamics.
We present a formulation of non-Markovian quantum trajectories for open systems from a measurement theory perspective. In our treatment there are three distinct ways in which non-Markovian behavior can arise: a mode-dependent coupling between the bath (reservoir) and system, a dispersive bath, and spectral detection of the output into the bath. In the first two cases the non-Markovian behavior is intrinsic to the interaction; in the third case the non-Markovian behavior arises from the method of detection. We focus in detail on the trajectories that simulate real-time spectral detection of the light emitted from a localized system. In this case the non-Markovian behavior arises from the uncertainty in the time of emission of particles that are later detected. The results of computer simulations of the spectral detection of the spontaneous emission from a strongly driven two-level atom are presented.