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arXiv:quant-ph/0510127 · Physical Review Letters

Theory of Decoherence due to Scattering Events and Lévy Processes

Bassano Vacchini

Published Nov 28, 2005• 35 citations
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Abstract

A general connection between the characteristic function of a Lévy process and loss of coherence of the statistical operator describing the center of mass degrees of freedom of a quantum system interacting through momentum transfer events with an environment is established. The relationship with microphysical models and recent experiments is considered, focusing on the recently observed transition between a dynamics described by a compound Poisson process and a Gaussian process.

DOI
10.1103/physrevlett.95.230402

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A general connection between the characteristic function of a Lévy process and loss of coherence of the statistical operator describing the center of mass degrees of freedom of a quantum system interacting through momentum transfer events with an environment is established. The relationship with microphysical models and recent experiments is considered, focusing on the recently observed transition between a dynamics described by a compound Poisson process and a Gaussian process.
Translation-covariant Markovian master equations used in the description of decoherence and dissipation are considered in the general framework of Holevo's results on the characterization of generators of covariant quantum dynamical semigroups. A general connection between the characteristic function of classical Lévy processes and loss of coherence of the statistical operator describing the center of mass degrees of freedom of a quantum system interacting through momentum transfer events with an environment is established. The relationship with both microphysical models and experimental realizations is considered, focusing in particular on recent interferometric experiments exploring the boundaries between classical and quantum world.
Translation-covariant Markovian master equations used in the description of decoherence and dissipation are considered in the general framework of Holevo’s results on the characterization of generators of covariant quantum dynamical semigroups. A general connection between the characteristic function of classical Lévy processes and loss of coherence of the statistical operator describing the center of mass degrees of freedom of a quantum system interacting through momentum transfer events with an environment is established. The relationship with both microphysical models and experimental realizations is considered, focusing in particular on recent interferometric experiments exploring the boundaries between classical and quantum world.
We point out that a unified theoretical framework for the explanation of quite different decoherence experiments can be outlined, provided the interaction causing decoherence can be described in terms of scattering events corresponding to random momentum transfers between system and environment. This unified description relies on a direct correspondence between the different possible master-equations describing such decoherence dynamics and the classical Lévy-Khintchine formula. The loss of coherence due to interaction with the environment is then described in terms of the characteristic function of the related Lévy process, accounting for a wide range of different possible behaviours.
The phenomenon of decoherence appears when the quantum behaviour of a microsystem is investigated. If the shielding of the considered microsystem from the macroscopic environment is not perfect, typical quantum features, such as the capability to exhibit quantum fringes, are suppressed as an unavoidable result of the interaction with the macroscopic background. Focusing on the centre of mass degrees of freedom of a massive test particle decoherence can typically be described in terms of random momentum transfers with the environment, thus naturally calling for a probabilistic standpoint. In this framework a general connection between the characteristic function of a Lévy process and loss of coherence of a massive quantum system interacting through momentum transfer events with an environment will be put into evidence, relying on Holevo’s characterization of quantum dynamical semigroups in the presence of translational invariance. The relationship with microphysical models and recent experiments on decoherence will also be considered.
Quantum systems are unavoidably open to their surrounding degrees of freedom. The theory of open quantum systems is thus crucial to understanding the fluctuations, dissipation, and decoherence of a quantum system of interest. Typically, the bath is modeled as an ensemble of harmonic oscillators, which yields Gaussian statistics of the bath influence on the quantum systems. However, there are also phenomena in which the bath consists of two-state systems, spins, or anharmonic oscillators; therefore, the non-Gaussian properties of the bath become important. Nevertheless, a theoretical framework to describe quantum systems under the influence of such non-Gaussian baths is not well established. Here, we develop a theory to describe quantum dissipative systems affected by Poisson noise properties of the bath, because the Lévi-Itô decomposition theorem asserts that Poisson noise is fundamental in describing arbitrary white noise beyond Gaussian properties. We introduce a quantum bath model that allows for the consistent description of dissipative quantum systems. The obtained master equation reveals non-Gaussian bath effects in the white noise regime, and provides an essential step toward describing open quantum dynamics under the influence of generic baths.
The interaction of a quantum system with a many degree of freedom environment entails damping and the loss of quantum coherence. In these two lectures we focus on two aspects of open quantum system dynamics. First, we present decoherence as a dynamical phenomenon and determine the corresponding time scales, discuss an experiment and the nature of robust states, and mention universal properties of short-time decoherence of macroscopic superpositions. Secondly, in analogy to the classical description of open systems in terms of Langevin equations, we present a stochastic approach to open quantum system dynamics in terms of a stochastic Schrödinger equation. We give a microscopic derivation that allows us to generalize the stochastic approach to non-Markovian situations. We discuss a convolutionless formulation of our theory and finally, we focus on the quantised version of Brownian motion as an often-employed example.