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Physical Review Letters

Two-Photon Excitation of Autoionizing States through Zeros in the Continuum

Thomas F. Gallagher, Ravinder Kachru, Nam Huu Tran, H. B. van Linden van den Heuvell

Published Nov 7, 1983• 27 citations
Publisher

Abstract

A method is described for two-photon excitation of autoionizing states by use of two different-frequency photons in which the first photon reaches an energy which is near a maximum in the one-photon cross section but where the one-photon cross section is very nearly zero. This provides a large two-photon amplitude while suppressing the single-photon excitation. The application of the technique to study the Ba $6snd\ensuremath{-}7snd$ transitions by detecting the total ionization produced is described. No discrimination between ionization from one- and two-photon processes was required.

DOI
10.1103/physrevlett.51.1753

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A method is described for two-photon excitation of autoionizing states by use of two different-frequency photons in which the first photon reaches an energy which is near a maximum in the one-photon cross section but where the one-photon cross section is very nearly zero. This provides a large two-photon amplitude while suppressing the single-photon excitation. The application of the technique to study the Ba 6snd\ensuremath−7snd6snd\ensuremath{-}7snd6snd\ensuremath−7snd transitions by detecting the total ionization produced is described. No discrimination between ionization from one- and two-photon processes was required.
Stimulated by a recent measurement of coherent control in photoionization of atomic barium, we have calculated one- and two-photon ionization cross sections of the aligned 6s6p 1P16s6p\text{ }{^{1}P}_{1}6s6p 1P1​ state of barium in the energy range between the 5d3/25{d}_{3/2}5d3/2​ and 5d5/25{d}_{5/2}5d5/2​ states of Ba+{\text{Ba}}^{+}Ba+. We have also measured these photoionization spectra in the same energy region, driving the one- or two-photon processes with the second or first harmonic of a tunable dye laser, respectively. Our calculations employ the eigenchannel RRR-matrix method and multichannel quantum defect theory to calculate the rich array of autoionizing resonances in this energy range. The nonresonant two-photon process is described using lowest-order perturbation theory for the photon-atom interactions, with a discretized intermediate-state one-electron continuum. The calculations provide an absolute normalization for the experiment, and they accurately reproduce the rich resonance structures in both the one- and two-photon cross sections, and confirm other aspects of the experimental observations. These results demonstrate the ability of these computationally inexpensive methods to reproduce experimental observables in one- and two-photon ionization of heavy alkaline earths, and they lay the groundwork for future studies of the phase-controlled interference between one- and two-photon ionization processes.
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.
In the present study we have investigated three-photon ionization in Ca in which autoionizing states are engaged. The two-photon resonant process (from the Ca ground state 4s 2 1 S 0 ) occurred through or at least in the vicinity of one of the following states: 4s4d 1 D 2 , 4p 2 3 P 2 , 4s6s 1 S 0 , 4p 2 1 D 2 and 4p 2 1 S 0 , with the third photon either reaching the continuum directly or one of the autoionizing states. The three-photon resonant transitions to 3d m p, m f: 1 P 1 , 3 P 1 and 3 D 1 autoionizing states for m up to 21 have been observed. Some of the autoionizing resonances which we have found had not been observed before in a high-resolution one-photon absorption experiment (for J = 1) and in multiphoton experiments (for J = 3). We have compared the ionization signal as a function of the laser detuning and the laser intensity with theoretical curves obtained within a simple model (three-level atom + one-mode laser field). This gives information about the order of magnitude of the three-photon ionization probability through autoionizing states.
Two-step resonant photoionization of free Ni atoms is studied by one-color and two-color processes, using pulsed lasers with photon energies around half the ground-state ionization energy. Two-color two-step resonance ionization from the ground state a3{\mathrm{}}^{3}3F4{\mathit{F}}_{4}F4​ and the first metastable state a3{\mathrm{}}^{3}3D3{\mathit{D}}_{3}D3​ via the triplet states z3{\mathrm{}}^{3}3G3,4,50{\mathit{G}}_{3,4,5}^{0}G3,4,50​ was used to probe the autoionizing states just above the ionization limit. Several strong lines in the one-color ionization spectrum are explained as direct two-photon transitions to autoionizing states. Photoionization cross sections were deduced from saturation measurements. The large cross sections observed for specific one-color two-step transitions are due to the near double resonant excitation into autoionizing states. \textcopyright{} 1996 The American Physical Society.
We report the excitation of highly excited 6d52(32)nd(ns)6{d}_{\frac{5}{2}(\frac{3}{2})}\mathrm{nd}(\mathrm{ns})6d25​(23​)​nd(ns) states of barium, which lie ~5.6 eV above the first ionization limit of Ba, using two-photon excitation from the bound 6snd(ns)6snd(\mathrm{ns})6snd(ns) Rydberg states. The two-photon excitation scheme requires rather modest laser power (~0.5 mJ), and the (6d52ndj)J=4{(6{d}_{\frac{5}{2}}n{d}_{j})}_{J=4}(6d25​​ndj​)J=4​ states exhibit a sharp enhancement in the autoionization rate beyond n=25n=25n=25 which is accompanied by the onset of ejection of very-low-energy electrons ( 0.02 eV). We observe that the 6d52ndj)J=4(n25){6{d}_{\frac{5}{2}}n{d}_{j})}_{J=4}(n25)6d25​​ndj​)J=4​(n25) states predominantly autoionize to the nearly degenerate 6d(32)6{d}_{(\frac{3}{2})}6d(23​)​ state of Ba+{\mathrm{Ba}}^{+}Ba+. This result has important implications for the development of autoionization lasers and the phenomenon of dielectronic recombination.
Measurements of the absolute generalized cross sections for the non-resonant two-photon excitation of discrete states of barium atoms are presented. They are based on the detection of an ion current due to absorption of a third photon in two processes of both resonant and non-resonant two-photon excitation of the same discrete level. Also considered is the appearance of additional lines in the two-photon absorption spectrum due to superradiance of the dye laser, the anomalous width of some of the two-photon resonances and the use of two-photon resonances for calibration purposes in investigation of autoionization resonances.