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Bulletin of the Lebedev Physics Institute

Analysis of Multiphoton Transitions within the Two-Level Scheme

Tatiana I. Kuznetsova

Published Dec 1, 2022• 0 citations
Publisher

Abstract

Abstract The contribution of a single pair of energy levels to multiphoton absorption under pulsed optical pumping is discussed. A simplified model is proposed to describe multiphoton ionization, which allows approximate estimates of the process rate as a function of system parameters.
DOI
10.3103/s1068335622120065

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The short-time behavior of atomic multiphoton-ionization profiles is investigated using simplified models of the field and the atom. The importance of including many levels in the model atom, of spontaneous emission, and of pulse shape are studied in detail. It is shown that the first two of these have little influence on the qualitative behavior of the short-time behavior of the resonance profile, but that the third, the pulse shape, is critical in determining the time evolution of the resonance profile.
A general framework for description of quantum systems in strong external fields is established. The most important application of the theory is concerned with the multiphoton ionization of atoms and molecules. The adiabatic approximation is developed. The Hamiltonian of the system is diagonalized by a time-dependent unitary transformation, which generates an interaction energy vanishing for very slow fields. A general analysis of the photoionization rates is performed. A specific model is considered: one-dimensional motion in the δ-function potential and external harmonic electric field. This model allows the exact solution for time-dependent eigenvalues and eigenfunctions. These solutions are compared with the conventional free electron approach to the ionization states.
Excitation of an atomic system subjected to a slowly varying external electromagnetic field is studied using a two-level model. Time evolution of the system is found using an approach which is nonperturbative in the field strength. There is no constraint to small values of the applied field, that is, the field (in appropriate energy units) need not be small compared to the difference in energies of the two levels. Rather, we use the fact that the situation of interest to us is where the frequency of the exciting field is small compared to the frequency associated with the level difference. Transition probabilities and resonance conditions are found which circumscribe both the large- and small-field limits. In the weak-field limit the previous results of high-order perturbation theory are readily recovered. For a monochromatic field the characteristic features of resonance excitation at high harmonic number of the applied field are (a) extremely narrow resonance widths and (b) shifts in resonance positions which are strong functions of field intensity. Because of this sensitivity, we are able to demonstrate that when slow temporal evolution of the field amplitude is taken into account (e.g., due to finite pulse duration) the appropriate mean excitation rate is that due to the uncorrelated contribution of many resonances. The results of this analysis are used to estimate excitation rates in a specific atomic system, Cd12+{\mathrm{Cd}}^{12+}Cd12+, which are then compared to multiphoton-ionization rates. Our calculations suggest that the ionization rate exceeds the excitation rate by several orders of magnitude.