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arXiv:0811.1596 · International Journal of Modern Physics A

DECOHERENCE AND RECOHERENCE IN MODEL QUANTUM SYSTEMS

Jen-Tsung Hsiang, L. H. FORD

Published Apr 9, 2009• 9 citations
arXivHTMLPDF

Abstract

We discuss the various manifestations of quantum decoherence in the forms of dephasing, entanglement with the environment, and revelation of "which-path" information. As a specific example, we consider an electron interference experiment. The coupling of the coherent electrons to the quantized electromagnetic field illustrates all of these versions of decoherence. This decoherence has two equivalent interpretations, in terms of photon emission or in terms of Aharonov-Bohm phase fluctuations. We consider the case when the coherent electrons are coupled to photons in a squeezed vacuum state. The time-averaged result is increased decoherence. However, if only electrons which are emitted during selected periods are counted, the decoherence can be suppressed below the level for the photon vacuum. This is the phenomenon of recoherence. This effect is closely related to the quantum violations of the weak energy condition, and is restricted by similar inequalities. We give some estimates of the magnitude of the recoherence effect and discuss prospects for observing it in an electron interferometry experiment.

DOI
10.1142/s0217751x09045273

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We discuss the various manifestations of quantum decoherence in the forms of dephasing, entanglement with the environment, and revelation of "which-path" information. As a specific example, we consider an electron interference experiment. The coupling of the coherent electrons to the quantized electromagnetic field illustrates all of these versions of decoherence. This decoherence has two equivalent interpretations, in terms of photon emission or in terms of Aharonov-Bohm phase fluctuations. We consider the case when the coherent electrons are coupled to photons in a squeezed vacuum state. The time-averaged result is increased decoherence. However, if only electrons which are emitted during selected periods are counted, the decoherence can be suppressed below the level for the photon vacuum. This is the phenomenon of recoherence. This effect is closely related to the quantum violations of the weak energy condition, and is restricted by similar inequalities. We give some estimates of the magnitude of the recoherence effect and discuss prospects for observing it in an electron interferometry experiment.
The interference pattern of coherent electrons is effected by coupling to the quantized electromagnetic field. The amplitudes of the interference maxima are changed by a factor which depends upon a double line integral of the photon two-point function around the closed path of the electrons. The interference pattern is sensitive to shifts in the vacuum fluctuations in regions from which the electrons are excluded. Thus this effect combines aspects of both the Casimir and the Aharonov-Bohm effects. The coupling to the quantized electromagnetic field tends to decrease the amplitude of the interference oscillations, and hence is a form of decoherence. The contributions due to photon emission and to vacuum fluctuations may be separately identified. It is to be expected that photon emission leads to decoherence, as it can reveal which path an electron takes. It is less obvious that vacuum fluctuations also can cause decoherence. What is directly observable is a shift in the fluctuations due, for example, to the presence of a conducting plate. In the case of electrons moving parallel to conducting boundaries, the dominant decohering influence is that of the vacuum fluctuations. The shift in the interference amplitudes can be of the order of a few percent, so experimental verification of this effect may be possible. The possibility of using this effect to probe the interior of matter, e.g., to determine the electrical conductivity of a rod by means of electrons encircling it is discussed. (Presented at the Conference on Fundamental Problems in Quantum Theory, University of Maryland, Baltimore County, June 18-22, 1994.)
We review different attempts to show the decoherence process in double-slit-like experiments both for charged particles (electrons) and for neutral particles with permanent dipole moments. Interference is studied when electrons or atomic systems are coupled to classical or quantum electromagnetic fields. The interaction between the particles and time-dependent fields induces a time-varying Aharonov phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be almost as large as the corresponding one for coherent electrons and therefore can be observed. We analyse different trajectories in order to show the dependence of the decoherence factor on the velocity of the particles.
The coupling of the quantized electromagnetic field to coherent electrons is investigated. The effects both of photon emission and of the electromagnetic vacuum fluctuations upon electron interference are analyzed. The modifications of the vacuum fluctuations due to a conducting plate lead to a decrease in the amplitude of the interference oscillations. The possibility of observing this effect is discussed. It is also shown that there is an analogue of the Aharonov-Bohm effect in which electron interference is sensitive to vacuum fluctuations in regions from which the electrons are excluded.
This work presents Version 2.0 of Quantum Decoherence and Conditional Recoherence as Loss and Restoration of Shared Phase Influence, a clarification and extension of standard decoherence theory within orthodox quantum mechanics.The paper reframes quantum decoherence as the physical loss of shared phase influence between components of a quantum system due to unavoidable entanglement with environmental degrees of freedom. Using standard density-matrix and system–environment coupling formalisms, decoherence is shown to correspond to dispersal of phase information into the environment rather than destruction of quantum states or invocation of fundamental wavefunction collapse.Conditional recoherence is treated within the same framework, demonstrating that restoration of coherence is possible only under constrained physical conditions where phase information has not irreversibly propagated into uncontrolled environmental modes. Known mechanisms such as spin-echo refocusing, dynamical decoupling, and quantum error correction are shown to be consistent with this interpretation.This Version 2.0 manuscript emphasizes structural clarity over speculative interpretation. It preserves unitary quantum dynamics, avoids observer-dependent or consciousness-based claims, and remains fully compatible with open-quantum-system formalisms including Lindblad-type master equations. The work provides a clearer physical account of measurement, irreversibility, and classical emergence without introducing new forces or modifying established quantum theory.The manuscript is intended for researchers and educators working in quantum foundations, open quantum systems, and quantum information theory, and is suitable for citation and pedagogical use.
The problem of quantum interference in the presence of an environment is considered by two approaches. One treats the problem from the point of view of the trace left by the interfering particle on its environment. The other regards the phase accumulation of the interfering waves as a statistical process, and explains the loss of interference in terms of uncertainty in the relative phase. The equivalence of the two approaches is proven for the general case. The two approaches are applied to dephasing of electron interference by photon modes in coherent and thermal states, and to dephasing by electromagnetic fluctuations in metals.
The article examines the problem of physical interpretation of quantum decoherence, which is traditionally described within phenomenological models of interaction between a quantum system and its environment. It is shown that standard approaches effectively reproduce the dynamics of phase damping but do not provide an explanation of the physical origin of coherence loss. A temporal interpretation of decoherence is proposed, in which phase damping is considered as a consequence of disruption of time synchronization in an inhomogeneous temporal environment. The paper demonstrates that the proposed approach is formally consistent with the density matrix formalism and Lindblad-type equations, reproducing standard exponential decoherence laws. It is substantiated that stochastic and non-Markovian effects can be interpreted as manifestations of temporal correlations and slow temporal drift. The practical value of the research lies in the possibility of applying the proposed interpretation to analyze noise, memory effects, and phase dynamics stability in complex information and quantum systems.