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Physical Review A

Semiclassical interaction of multilevel atoms with monochromatic electromagnetic fields

Alfred M. Levine, W. M. Schreiber, Andrei N. Weiszmann

Published Feb 1, 1982• 15 citations
Publisher

Abstract

The solution of the time-dependent Hamiltonian for the semiclassical dipole interaction of a multilevel atom with monochromatic electromagnetic fields is presented. Characteristics of the eigenvalue equation are investigated. Results are presented for the interaction of unequally spaced multilevel atoms with multiple monochromatic electromagnetic fields. The connection with the quantized-field method is discussed. Complications due to atomic decay are included only in the final discussion.

DOI
10.1103/physreva.25.625

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Cambridge University Press eBooks•Sep 4, 1997•5 citations
The solution of the time-dependent Hamiltonian for the semiclassical dipole interaction of a multilevel atom with monochromatic electromagnetic fields is presented. Characteristics of the eigenvalue equation are investigated. Results are presented for the interaction of unequally spaced multilevel atoms with multiple monochromatic electromagnetic fields. The connection with the quantized-field method is discussed. Complications due to atomic decay are included only in the final discussion.
The dynamical behavior of the dipole interaction of an equally spaced multilevel atom is analyzed. The atom has a spinlike distribution of dipole transition moments and interacts with a single-mode radiation field. Detailed results for three-level (J=1J=1J=1) and four-level (J=32J=\frac{3}{2}J=23​) systems are presented.
An improved form of semiclassical radiation theory is developed which includes the effect of the atom's radiation field back on the atom. This formalism is applied to the problem of a single two-level atom interacting with a monochromatic field. The resulting equations are solved without resorting to time-dependent perturbation theory, and are found to predict the behavior of the system over times long compared with the lifetime for spontaneous transitions. Not only stimulated emission and absorption, but also spontaneous emission with the proper Einstein AAA coefficient, and a frequency shift which agrees at least semiquantitatively with the Lamb shift are described. In addition, several nonlinear effects involving the interference between spontaneous and stimulated radiation are described, and new experiments which might detect such effects are suggested.
An improved form of semiclassical radiation theory is developed which includes the effect of the atom's radiation field back on the atom. This formalism is applied to the problem of a single "two-level atom" interacting with a monochromatic field. The resulting equations are solved without resorting to time-dependent perturbation theory, and are found to predict the behavior of the system over times long compared with the lifetime for spontaneous transitions. Not only stimulated emission and absorption, but also spontaneous emission with the proper Einstein AAA coefficient, and a frequency shift which agrees at least semiquantitatively with the Lamb shift are described. In addition, several nonlinear effects involving the interference between spontaneous and stimulated radiation are described, and new experiments which might detect such effects are suggested.
One of the simplest nontrivial problems involving the atom–field interaction is the coupling of a two-level atom with a single mode of the electromagnetic field. A two-level atom description is valid if the two atomic levels involved are resonant or nearly resonant with the driving field, while all other levels are highly detuned. Under certain realistic approximations, it is possible to reduce this problem to a form which can be solved exactly; allowing essential features of the atom-field interaction to be extracted. In this chapter we present a semiclassical theory of the interaction of a single two-level atom with a single mode of the field in which the atom is treated as a quantum two-level system and the field is treated classically. A fully quantum mechanical theory will be presented in Chapter 6. A two-level atom is formally analogous to a spin-1/2 system with two possible states. In the dipole approximation, when the field wavelength is larger than the atomic size, the atom–field interaction problem is mathematically equivalent to a spin-1/2 particle interacting with a time-dependent magnetic field. Just as the spin-1/2 system undergoes the so-called Rabi oscillations between the spin-up and spin-down states under the action of an oscillating magnetic field, the two-level atom also undergoes optical Rabi oscillations under the action of the driving electromagnetic field. These oscillations are damped if the atomic levels decay. An understanding of this simple model of the atom–field interaction enables us to consider more complicated problems involving an ensemble of atoms interacting with the field.