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arXiv:quant-ph/0612192 · Physical Review A

Loss of coherence and dressing in QED

Bruno Bellomo, G. Compagno, Francesco Petruccione

Published Nov 22, 2006• 6 citations
arXivHTMLPDF

Abstract

The dynamics of a free charged particle, initially described by a coherent wave packet, interacting with an environment, i.e., the electromagnetic field characterized by a temperature $T$, is studied. Using the dipole approximation, the exact expressions for the evolution of the reduced density matrix both in momentum and configuration space and the vacuum and the thermal contribution to decoherence are obtained. The time behavior of the coherence lengths in the two representations are given. Through the analysis of the dynamic of the field structure associated with the particle the vacuum contribution is shown to be linked to the birth of correlations between the single momentum components of the particle wave packet and the virtual photons of the dressing cloud.

DOI
10.1103/physreva.74.052112

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The dynamics of a free charged particle, initially described by a coherent wave packet, interacting with an environment, i.e., the electromagnetic field characterized by a temperature TTT, is studied. Using the dipole approximation, the exact expressions for the evolution of the reduced density matrix both in momentum and configuration space and the vacuum and the thermal contribution to decoherence are obtained. The time behavior of the coherence lengths in the two representations are given. Through the analysis of the dynamic of the field structure associated with the particle the vacuum contribution is shown to be linked to the birth of correlations between the single momentum components of the particle wave packet and the virtual photons of the dressing cloud.
We consider the dynamics of a charged free particle, initially described by a coherent wave packet, interacting with an electromagnetic field characterized by the temperature T, considered as the environment. We have used dipole approximation neglecting the potential vector quadratic term in the minimal coupling Hamiltonian. This leads to the loss of coherence in the momentum representation, described by the decay of the off diagonal elements of the particle reduced density matrix, while the populations remain constant. Here we extend the analysis to the coordinate representation. We compute the particle reduced density matrix in this basis, analyzing in particular the mixing of various effects, such as free spreading, vacuum dressing and vacuum and thermal decoherence, in the wave packet width and coherence length evolution.
We consider the development of decoherence between the momentum components of a wave packet of a non relativistic charged particle interacting linearly with the electromagnetic field in equilibrium at temperature T. By adopting from the beginning the electric dipole approximation the Hamiltonian assumes a form analogous to the one used in the context of quantum computing for an ensemble of two level systems. We obtain the characteristic vacuum and thermal decoherence times and we show that decoherence between different momenta is due to the onset of a correlation between each momentum component and the associated transverse photons that are also responsible of mass renormalization.
We consider a free charged particle interacting with an electromagnetic bath at zero temperature. The dipole approximation is used to treat the bath wavelengths larger than the width of the particle wave packet. The effect of these wavelengths is described then by a linear Hamiltonian whose form is analogous to phenomenological Hamiltonians previously adopted to describe the free particle-bath interaction. We study how the time dependence of decoherence evolution is related with initial particle-bath correlations. We show that decoherence is related to the time dependent dressing of the particle. Moreover because decoherence induced by the T=0 bath is very rapid, we make some considerations on the conditions under which interference may be experimentally observed.
Abstract In quantum electrodynamics, the matter degrees of freedom are coupled to the radiation field through a local, gauge-invariant interaction density. Due to the linear structure of this coupling, the problem of constructing a complete formal representation of the reduced matter dynamics can be solved exactly if the electromagnetic radiation field is initially in a Gaussian state. This chapter combines field theoretical methods with superoperator and influence functional techniques to derive an exact, relativistic representation for the reduced density matrix of the matter degrees of freedom which completely describes the influence of the electromagnetic radiation field on the matter dynamics. Several applications are treated, such as the suppression of the quantum coherence of charged particles caused by the emission of bremsstrahlung and the decoherence of many-particle states.
We find an exact analytical solution of the reduced density matrix from the Feynman-Vernon influence functional theory for a wave packet influenced by an environment containing a few discrete modes. We obtain two intrinsic energy scales relating to the time scales of the system and the environment. Different relationship between these two scales alters the overall form of the solution of the system. We also introduce a decoherence measure for a single wave packet which is defined as the ratio of Schrödinger uncertainty over the delocalization extension of the wave packet and characterizes the time-evolution behavior of the off-diagonal reduced density matrix element. We utilize the exact solution and the docherence measure to study the wave packet decoherence dynamics. We further demonstrate how the dynamical diffusion of the wave packet leads to non-Markovian decoherence in such a microscopic environment.
The emergence of decoherence in quantum electrodynamics is investigated. On combining superoperator methods with functional techniques from field theory, the degrees of freedom of a thermal radiation field are eliminated and the influence phase functional is derived which governs the reduced dynamics of the matter variables. Employing a prototypical interference device, a decoherence functional is developed which provides a gauge invariant relativistic measure for the degree of decoherence. It is demonstrated that the decoherence functional describes the destruction of quantum coherence through the emission of bremsstrahlung which is caused by the relative motion of the interfering components of a superposition. Explicit analytical expressions for the vacuum and the thermal contribution to the decoherence functional and for the corresponding coherence lengths are determined. These expressions reveal that bremsstrahlung leads to a fundamental decoherence mechanism which dominates for short times and which is present even in the electromagnetic field vacuum at zero temperature. The influence of bremsstrahlung on the center of mass coordinate of a system of many identical charged particles is also studied and is shown to lead to a strong suppression of quantum coherence.