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Physical Review A

Multiphoton ionization of helium under uv radiation: Role of the harmonics

Lampros A. A. Nikolopoulos, P. Lambropoulos

Published Dec 15, 2006• 15 citations
Publisher

Abstract

We present a quantitative theory with detailed calculations pertaining to multiphoton ionization of helium under moderately strong uv radiation of photon energy $13\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Employing both, the nonperturbative solution of the time-dependent Schr\"odinger equation, as well as perturbation theory, we obtain detailed results for all processes expected to be of quantitative relevance within the range of intensities and pulse durations in this work, which have been chosen so as to match the conditions of a recent experiment on exactly this problem [T. Laarman et al., Phys. Rev. A 72, 023409 (2005)]. The conclusion, in connection with the experimental data, which our results lead to is that, without the presence of the second harmonic of the fundamental in the radiation, it is impossible to reconcile the reported observations with fundamental features of the processes involved. A more general conclusion seems to be that the presence of these harmonics, even at intensities less than 1% of that of the fundamental, are apt to produce profound side effects that will mask multiphoton processes by the fundamental.

DOI
10.1103/physreva.74.063410

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We present a quantitative theory with detailed calculations pertaining to multiphoton ionization of helium under moderately strong uv radiation of photon energy 13eV13\phantom{\rule{0.3em}{0ex}}\mathrm{eV}13eV. Employing both, the nonperturbative solution of the time-dependent Schr"odinger equation, as well as perturbation theory, we obtain detailed results for all processes expected to be of quantitative relevance within the range of intensities and pulse durations in this work, which have been chosen so as to match the conditions of a recent experiment on exactly this problem [T. Laarman et al., Phys. Rev. A 72, 023409 (2005)]. The conclusion, in connection with the experimental data, which our results lead to is that, without the presence of the second harmonic of the fundamental in the radiation, it is impossible to reconcile the reported observations with fundamental features of the processes involved. A more general conclusion seems to be that the presence of these harmonics, even at intensities less than 1% of that of the fundamental, are apt to produce profound side effects that will mask multiphoton processes by the fundamental.
We present a theoretical study of the main characteristics of two-color photoionization spectra obtained when atoms are subjected to an intense radiation pulse containing the fundamental of an infrared laser and one of its higher harmonics. The frequency of the latter is chosen to be high enough that the atom can be ionized by a single photon. The calculation is performed by numerical integration of the time-dependent Schrödinger equation for a (three-dimensional) hydrogen atom. We present the general properties of the spectra and angular distributions as well as the possible occurrence of interferences between the laser-assisted process and above-threshold ionization. Our results indicate that such interference effects, which can lead to partial coherent control of the photoionization process, can be observed at moderate laser intensities within the reach of currently operated laser and harmonic sources.
The time-dependent Schr\"odinger equation for the helium atom with a model potential is solved on a numerical grid. The effects of intermediate-state resonance and of the ionization of the atom upon the harmonic generation are investigated. We also evaluate the contribution of the helium ion when the laser intensity is sufficiently high for most of the atoms to be ionized during the laser pulse. We find that the harmonics with order higher than 13 are due to the ion when the photon energy is 5.0 eV, while for photon energy 2.0 eV the atom produces up to about the 49th harmonic.
An approximate non-perturbative theory of multiphoton ionization of a hydrogen atom by two strong radiation fields is outlined. The special case is then considered for when one of the fields is of low intensity and high frequency and the other field is of high intensity and low frequency. A set of representative calculations has been performed for this case; that is, (a) angular distributions for given numbers of absorbed and emitted low-frequency photons and different geometries; (b) total cross-sections versus the strong-field intensity; (c) angular distributions summed over all the low-frequency photon exchanges, showing a fourfold symmetry in a geometry in which each ionization channel exhibits, instead, only a twofold symmetry; (d) the average energy gained by the ejected electrons. Calculations are performed for a strong low-frequency field of arbitrary polarization. In many respects, the present calculations are expected to complement those of single-field multiphoton ionization. It is hoped that the results of the calculations reported here may prompt systematic measurements also in this new class of processes, as the predictions are well within the state of the art of present multiphoton-ionization experiments.
A simple, "exactly solvable" atomic model will be presented that helps to discuss some of the interesting features of multiphoton ionization of atoms. The electromagnetic field is treated non-perturbatively, it can be strong. The atomic electrons are assumed to be non-interacting (Hartree model). They are bound in a harmonic oscillator potential (one- or three-dimensional). At the ionization energy, the potential is cut off and the free electron has no Coulomb attraction. The Schrodinger equation has exact analytic solutions valid in the inner or outer regions. If the field is turned on adiabatically, the exact solution can be found by matching these solutions at the boundary; both of their value and the normal derivative at all times. Thus the machine calculation reduces to repeated application of fast Fourier transforms and to the solution of linear equations (unfortunately a lot of them).
The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order 108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2) is determined by the intensity-dependent level width (6f6f6f configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order 1012{10}^{12}1012 W/cm2{\mathrm{cm}}^{2}cm2) are determined by both the intensity-dependent widths and shifts as‘\stackrel{\mathrm{`}}{\mathrm{s}}s‘ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.
We report on the experimental estimation of a lower bound of helium. Our experiment differs from a previous one described by Hasegawa et al. [Phys. Rev. A 71, 023407 (2005)]. The photons that correspond to the 27th harmonic of a Ti:sapphire laser have an energy of 41.8eV41.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}41.8eV. The extraction of the cross section rests on a theoretical model, based on the rate equations, that fully includes the contribution from the sequential channels and the macroscopic effects. Some of the experimental parameters are very difficult to measure accurately. For those parameters, we deliberately consider values compatible with their experimental determinations and that lead systematically to an underestimation of the two-photon double ionization cross section. Our estimation of this lower bound is higher than a bunch of various theoretical results. It stays, however, too close to these latter ones to draw any definite conclusion about their validity, even though it clearly indicates that the actual value of the double ionization cross section is higher than expected.