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Japanese Journal of Applied Physics

Spectroscopic Stability in Two-Photon Absorption by Atoms

Masataka Mizushima, Katsuhiko Nakahara, Tadashi Yoshida

Published Oct 1, 1989• 1 citation
Publisher

Abstract

When there exists no external field, physical results should not depend on the choice of quantization axis. This theorem is known as spectroscopic stability and is well established for one photon absorption and emission processes. In two photon absorption by a three level atom one can make the excitation of the top level forbidden if the absorption processes are restricted to one selection rule in Δ M (=+1, 0 or -1). The choice of selection rule assumes relative orientation between the polarization of the radiation field and an external field. If this relative orientation is changed the selection rule would also change and the top level would appear as a final result of two photon absorption . A question is what happens if the external field disappears in the latter case. Would the top level disappear although the selection rule stays unaltered? It is shown that the probability of having the top level disappears when the external field vanishes, confirming the spectroscopic stability and the degree of violation is obtained as a function of the strength of the external field.

DOI
10.1143/jjap.28.2018

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Three-photon bimolecular absorption is a process which, through the simultaneous absorption of three laser photons, results in the electronic excitation of two molecules or atoms. Following a recent treatment of the selection rules, a quantum electrodynamical treatment is employed to describe the main features associated with the process and to produce an equation for the excitation rate. The dependence on photon polarization is investigated, and the magnitude of the excitation rate is estimated. It is shown that two different mechanisms operate, each with different selection rules and different dependences on intermolecular separation. In each case an energy mismatch is conveyed from one molecule to the other by means of virtual photon coupling. Some possible schemes for experimental study of the process out outlined.
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So far we have treated the energy levels of an atomic system as stable states with infinite lifetimes. The presence of an electromagnetic field changes this picture. Absorption of photons will excite atoms and ions to higher levels, while stimulated emission will make excited ones decay. Einstein (1917) showed, using purely statistical arguments, that an excited ion will decay through spontaneous emission in the absence of an electromagnetic field. This process can also be derived by using a rigorous quantum electrodynamic treatment, where the field is quantized. In this chapter we start by discussing transitions between atomic levels in a general sense, postulating the operators responsible for the decay. After the first few sections we will concentrate on the most important few multipoles or terms in the expansion of the electromagnetic field. We will introduce a number of different properties describing the transition, and eventually arrive at the measurable transition rate and, directly linked to it, the lifetime of an excited state. We will start, however, with the most basic property, the component strength. Our aim is to arrive at computationally useful expressions as soon as possible. For a more thorough treatment of the theory of radiative transitions we refer to the book by Sobelman (1972). For a brief review of the many factors affecting spectra of atoms, see Martin and Wiese (1996) .
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