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Journal of Physics Conference Series

Dynamic effects of electromagnetic wave on a damped two-level atom: Exact solution via path integral

Mekki Aouachria, Farida Halimi

Published Apr 26, 2013• 3 citations
Publisher

Abstract

The spin coherent state path integral describing the dynamics of a two-level system interacting with electromagnetic wave of circular polarization is considered. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions. Then it is determined exactly using perturbation methods. Thus, the exact energy spectra with corresponding wave functions are deduced.

DOI
10.1088/1742-6596/435/1/012025

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The spin coherent state path integral describing the dynamics of a two-level system interacting with electromagnetic wave of circular polarization is considered. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions. Then it is determined exactly using perturbation methods. Thus, the exact energy spectra with corresponding wave functions are deduced.
The applications of the path integral formalism have widely increased since a large class of potentials have been resolved [1]. However, it is quite rare to find an explicit calculation for interactions that include spin [2]. As is commonly known, spin is a fundamental physical notion for the comprehension of atomic propertics. Recently, the behavior of a damped two-level atom with an electromagnetic wave of circular polarization has been studied using the Schrodinger equation approach [3]. The same problem has been considered without damping [4]. The purpose of this article is to deal with this same problem using the path integral formalism. The two-level atom with a mass m and an angular frequency ! has a dipole moment D. The dynamics of the atom in interaction with a wave is described by the following Hamiltonian:
Abstract We introduced the formalism of path integrals to describe the dynamics of a system consisting of two particles. One is located in a periodic potential well (first subsystem), while the other particle is outside the well and subjected to a circular electromagnetic field (second subsystem). Thanks to this formalism, we are able to describe the dynamics of our system by a propagator which is the product of two subsystems of propagators. The propagator of the first subsystem is put in the standard form exp[Action] as a result of the coherent spin states. This form of propagator is possible by replacing the spin with a unit vector aligned along the polar and azimuthal directions. The second subsystem propagator come with the use of the Feynman-Vernon functional on the subsystem. Thanks to its two propagators, we have succeeded in explicitly and analytically evaluating the dynamics of our dissipative quantum system by a single propagator. Using this fundamental result, we evaluated the special case where the second subsystem bathed in a super-ohmic environment.