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Journal of Physics B Atomic Molecular and Optical Physics

Classical computation of decoherence dynamics in continuous variable systems

Heekyung Han, Paul W. Brumer

Published Apr 18, 2007• 11 citations
Publisher

Abstract

The utility of classical mechanics to compute the dynamics of decoherence in continuous variable systems, as defined by the time dependence of the system purity, is examined. Its accuracy, in the semiclassical domain, is shown to depend on the nature of the coupling potentials and, less so, on the initial conditions. For a large range of cases, agreement between quantum and classical computations in small systems is shown to be excellent.

DOI
10.1088/0953-4075/40/9/s13

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The utility of classical mechanics to compute the dynamics of decoherence in continuous variable systems, as defined by the time dependence of the system purity, is examined. Its accuracy, in the semiclassical domain, is shown to depend on the nature of the coupling potentials and, less so, on the initial conditions. For a large range of cases, agreement between quantum and classical computations in small systems is shown to be excellent.
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This work studies the semiclassical behaviour of quantum models according to their dynamics. On the first part, we analyse quantum models with well defined classical limit and define a corresponding classical dynamics. We are intend to investigate here how those systems behave at this classical limit and how the quantum dynamics can be approximated. For that we make use of a semiclassical approximation as a systematic way of finding quantum corrections to the classical mean values of observables. We also make use of exact results for testing the semiclassical approximation for calculating typical quantum effects and the fidelity of the approximate state with the exact one. In the second part we deal with the classical limit of quantum mechanics through intercation with environment. The evolution of quantum and classical probability distributions are compared using the Wigner representation. We find then conditions under which the coupling of the system with the environment preserves two initially identical particles as identical and the we analyze the process of decoherence in that system.
We present a detailed report on the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments. The rate of decoherence is quantified by relating it to the decay rates of various, complementary measures of the quantum nature of a state, such as the purity, some non-classicality indicators in phase space, and, for two-mode states, entanglement measures and total correlations between the modes. Different sets of physically relevant initial configurations are considered, including one- and two-mode Gaussian states, number states, and coherent superpositions. Our analysis shows that, generally, the use of initially squeezed configurations does not help to preserve the coherence of Gaussian states, whereas it can be effective in protecting coherent superpositions of both number states and Gaussian wavepackets.
We present a detailed report on the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments. The rate of decoherence is quantified by relating it to the decay rates of various, complementary measures of the quantum nature of a state, such as the purity, some non-classicality indicators in phase space, and, for two-mode states, entanglement measures and total correlations between the modes. Different sets of physically relevant initial configurations are considered, including one- and two-mode Gaussian states, number states, and coherent superpositions. Our analysis shows that, generally, the use of initially squeezed configurations does not help to preserve the coherence of Gaussian states, whereas it can be effective in protecting coherent superpositions of both number states and Gaussian wavepackets.