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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Long-time behaviour of a two-level system in interaction with an electromagnetic field

Pierre Meystre, Edmond Geneux, A. Quattropani, A. Faist

Published Feb 1, 1975• 104 citations
Publisher
DOI
10.1007/bf02724735

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We consider a system formed by a two-level atom initially in its bare ground state and the electromagnetic field in the absence of radiation. The interaction of the atom with the radiation field leads to the formation of a dressed ground state. To describe the dynamics of self-dressing, we study the time evolution of the permanence amplitude in the initial state. We adopt non-relativistic QED and take the atom-field interaction Hamiltonian in the minimal coupling form, within the electric dipole approximation. In order to follow the evolution of the permanence amplitude for long enough time periods we use the van Hove resolvent technique with appropriate partial summation of Feynman graphs. We show that the self-dressing process presents the typical behaviour of a decay process and occurs with a timescale a *-1 , which is long compared with both the atom's inverse transition frequency 0 -1 and the excited state decay time -1 . This time is comparable with the lifetime of the excited state due to ordinary two-photon decay. We consider the reasons for such a long time period of self-dressing and make comparison with previous results.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 27, 1999•9 citations
The purpose of this paper is to demonstrate solutions of Schrödinger's equations for a two-level quantum system which is coupled to a radiation field. The electric (or magnetic) field, which is considered as a definite (if unknown) function of time E(t), is characterized by a power spectrum or its related correlation function. Long-time transition probabilities are obtained in the form of a contour integral under the assumption of small atom-field coupling. The contour integral can be easily evaluated for many cases of interest. In particular, it is shown how a two level system in interaction with a blackbody approaches the Maxwell-Boltzmann distribution as t → infin.
We consider a system formed by a two-level atom initially in its bare ground state and the electromagnetic field in the absence of radiation. The interaction of the atom with the radiation field leads to the formation of a dressed ground state. To describe the dynamics of self-dressing, we study the time evolution of the permanence amplitude in the initial state. We adopt non-relativistic QED and take the atom-field interaction Hamiltonian in the minimal coupling form, within the electric dipole approximation. In order to follow the evolution of the permanence amplitude for long enough time periods we use the van Hove resolvent technique with appropriate partial summation of Feynman graphs. We show that the self-dressing process presents the typical behaviour of a decay process and occurs with a timescale a *-1 , which is long compared with both the atom's inverse transition frequency 0 -1 and the excited state decay time -1 . This time is comparable with the lifetime of the excited state due to ordinary two-photon decay. We consider the reasons for such a long time period of self-dressing and make comparison with previous results.