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arXiv:quant-ph/0409167 · Journal of Physics A Mathematical and General

Initial correlations effects on decoherence at zero temperature

Bruno Bellomo, G Compagno, Francesco Petruccione

Published Nov 9, 2005• 6 citations
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Abstract

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.

DOI
10.1088/0305-4470/38/47/010

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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.
We study the effect of initial correlations on the short-time decoherence of a particle linearly coupled to a bath of harmonic oscillators. We analytically evaluate the attenuation coefficient of the superposition of two wave packets both for a free and a harmonically bound particle, with and without initial thermal correlations between the particle and the bath. While short-time decoherence appears to be independent of the system in the absence of initial correlations, we find on the contrary that, for initial thermal correlations, decoherence becomes system dependent even for times much shorter than the characteristic time of the system. The temperature behavior of this system dependence is discussed.
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 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 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.
Most discussions of decoherence in the literature consider the high temperature regime but it is also known that, in the presence of dissipation, decoherence can occur even at zero temperature. Whereas most previous investigations all assumed initial decoupling of the quantum system and bath, we consider that the system and environment are entangled at all times. Here, we discuss decoherence for a free particle in an initial Schrödinger cat state. Memory effects are incorporated by use of the single relaxation time model.
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.