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Physical Review Letters

Two-photon processes in real atoms

F. Robicheaux, Bo Gao

Published Nov 25, 1991• 13 citations
Publisher

Abstract

We present a general method for calculating two-photon processes in real atoms by a variant of the usual multichannel quantum-defect theory (MQDT). Most notably, this method enables us to describe processes in which a single photon has enough energy to ionize the atom (above-threshold processes). All effects of intermediate Rydberg series, continua, or autoionizing series are treated on an equal footing and with the same ease; the final state is also treated properly by standard MQDT. This method should also work for many three- or four-photon processes.

DOI
10.1103/physrevlett.67.3066

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We present a general method for calculating two-photon processes in real atoms by a variant of the usual multichannel quantum-defect theory (MQDT). Most notably, this method enables us to describe processes in which a single photon has enough energy to ionize the atom (above-threshold processes). All effects of intermediate Rydberg series, continua, or autoionizing series are treated on an equal footing and with the same ease; the final state is also treated properly by standard MQDT. This method should also work for many three- or four-photon processes.
Based on multichannel quantum-defect theory, a method to calculate and compile radiative transition processes for atoms (including highly ionized high-ZZZ atoms) is proposed. Through defining the renormalized transition matrix elements from initial eigenchannels to final eigenchannels, the transition processes between infinitely many initial states and infinitely many final states can be treated conveniently. As illustrative examples, we study the alkali-metal atoms in detail.
Detailed descriptions of one- and two-photon ionization are presented. We go beyond conventional perturbation theory to investigate the dynamics of both processes for a broad range of field intensities. The general theory of unstable decaying states is applied to the problem of one-photon ionization (the photoeffect). It is found that a non-trivial dependence of the transition dipole moment on the continuum state energy can lead to corrections to exponential decay, and even oscillations in the bound state population. As examples we consider the photoionization of hydrogen and atoms with autoionizing states. Only in the absence of autoionizing states corrections to exponential decay remain inconsequential for any experimentally relevant intensity. Our description of two-photon ionization is formulated in the Heisenberg picture. Besides the usual two-level atom projection operators we introduce explicitly the operators referring to the atomic continuum. By eliminating from the equations of motion the terms related to the electromagnetic self field as well as the terms referring to the continuum, transverse and longitudinal damping corresponding to spontaneous emission and photoionization is obtained. The use of field correlation functions allows us to account for the partial coherence of the applied field. We develop a technique to extract from the equations of motion a unique two-photon ionization rate. Such a characterization of the ionization process is not only instructive because of its simplicity, it is also in many cases completely satisfactory. The resulting general expression for the two-photon ionization rate is the central result of our treatment. From it we recover several familiar results in different limiting cases. In addition, our general rate expression provides the first description of the complete hierarchy of saturation effects that one should expect. We present a number of examples where we calculate the two-photon ionization rate as a function of the detuning, and where we emphasize the saturation and field correlation effects.
The theory of two-photon ionization of the alkali atoms is developed from the well-known perturbation formula for the second-order transition rate. Quantum defect Coulomb functions are used for both the negative and positive energy states. Spin-orbit splitting of the intermediate ppp states is taken into account. The results are presented as dispersion curves of the transition rate for photon energies between the two-photon and one-photon thresholds. Cesium is of particular interest because the photon energy for the second harmonic of ruby laser light falls very near the 10p2P3210{p}^{2}{P}_{\frac{3}{2}}10p2P23​​ level. For a photon energy of 3.57 eV, the transition rate (in cgs units) is found to be 2.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}49}$\ifmmode\times\else\texttimes\fi{}(photonflux)2{(\mathrm{photon}\mathrm{flux})}^{2}(photonflux)2.
We analyze in this paper the process of double-electron ejection through two-photon absorption from the fundamental state of helium. We focus on the case of photon energies close to 2 a.u., which marks the threshold between direct and sequential double-ionization regimes. We demonstrate the crucial role of two-photon excitation-plus-ionization process of ${\mathit{nlk}}^{\ensuremath{'}}{l}^{\ensuremath{'}}$ Rydberg series. We show that the latter channel must be taken into account in the theory in order to properly describe two-electron ejection. A simple expression is derived for the electron energy spectrum, leading to better insights into the physics underlying two-photon absorption close to the sequential threshold.
A general theory is developed to treat two-photon ionization through a single intermediate state in which an arbitrary degree of relaxation may occur. The method is set up to probe the parameters governing the relaxation, by determination of the angular distribution of photoelectrons. The method is applied to the ionization of Na atoms, through the 3p2P123p^{2}P_{\frac{1}{2}}3p2P21​​ and 3p2P323p^{2}P_{\frac{3}{2}}3p2P23​​ intermediate states.