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Chinese Journal of Physics

Spin Coherent State Path Integral for a Two-level Atom in an Electromagnetic Wave of Circular Polarization

Mekki Aouachria

Published Jun 1, 2011• 6 citations
OpenAlex

Abstract

We study the movement of a two-level atom in interaction with an electromagnetic wave of circular polarization using the path integral formalism. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar-azimuthal direction. Then we use the phase-space and rotations in the space of spin coherent states to simplify the calculations. Thus the exact wave functions of the system are deduced.

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Treatment of a Damped Two-level Atom in an Electromagnetic Wave by the Path Integral Formalism

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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:

Chinese Journal of Physics•Oct 1, 2002•4 citations
We study the movement of a two-level atom in interaction with an electromagnetic wave of circular polarization using the path integral formalism. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar-azimuthal direction. Then we use the phase-space and rotations in the space of spin coherent states to simplify the calculations. Thus the exact wave functions of the system are deduced.
Exact solutions of the neutral spinning particle in interaction with rotating magnetic field and a scalar potential using path integral formalism have been found. The propagator is first written in the standard Feynman form by replacing the spin by a unit vector aligned along the polar and azimuthal directions (θ φ). Then we use the phase-space and rotations in the space of spin coherent states to simplify the calculations. Thus the exact energy spectrum with a corresponding wave functions are deduced.
We adopt a coherent states path integral formalism to study the system of a two-level atom moving in a quantized traveling light field and a gravitational field. By using the phase space and some rotations in the space of coherent states, have enabled greatly simplify the calculations. The propagator is first written in a standard form, ∫Dpathexpi/ℏSpath, by replacing the spin with a unit vector aligned along the polar and azimuthal directions. Then, it is determined exactly due to the auxiliary equation which has a spacial function as a solution. The corresponding wave functions have been deduced by applying the principles of quantum mechanics. The results obtained are perfectly identical with those found by other standard methods.
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: