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Journal of Experimental and Theoretical Physics

Single-photon double ionization of an atom in a strong radiation field

Elena A. Volkova, A. M. Popov, Olga V. Tikhonova

Published Mar 1, 2002• 0 citations
Publisher

Abstract

Double ionization is studied by direct numerical integration of the time-dependent Schrödinger equation for a model two-electron system in the field of an electromagnetic wave in the case when the photon energy exceeds the energy required for the removal of both electrons of the atom. The probabilities of single-electron and double ionization are obtained as functions of the radiation intensity. The energy spectra and double pulse distributions of photoelectrons are analyzed. It is shown that single-photon ionization plays a significant role only in the limiting cases of weak and strong fields. The obtained results are used in an analysis of the contributions from different channels to the double-ionization process (in particular, for clarifying the role of the electron-electron interaction). The results of numerical calculations are compared with the analytic model of the phenomenon.

DOI
10.1134/1.1469152

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A one-dimensional model of a helium atom in an intense field of a femtosecond electromagnetic pulse has been constructed using the Hartree technique. “Exact” calculations have been compared to the approximations of “frozen” and “passive” electrons. A nonmonotonic dependence of the single-electron ionization probability on the radiation intensity has been detected. Minima in the ionization probability are due to multiphoton resonances between different atomic states due to the dynamic Stark effect. We suggest that the ionization suppression is due to the interference stabilization in this case.
The ionization of a model atom in a strong single-mode non-classical electromagnetic field is studied beyond the perturbation approach using the model of ``one discrete level + continuum'' for the atom. Explicit analytical expressions for the time-dependent probability of atomic ionization are obtained for different initial states of radiative field: Fock state, coherent wave packet, squeezed vacuum state. The results are compared to the ionization decay of discrete atomic level in a classical light field, and are analyzed for different mean number of radiative photons. The time-dependent distribution of the quantized field over photon number states is examined.
Using the analytically obtained solution of the Schrödinger equation for an electron in a quantized electromagnetic field, the ionization of an atom has been considered in the framework of a simple one-dimensional model. Expressions for the ionization rate and photoelectron spectrum have been derived and analyzed. We discuss a difference between the results obtained in the model in which the electromagnetic field is described classically and the results obtained in the model of quantized electromagnetic field. In particular, in the latter model the photoelectron spectrum can have a minimum at a certain number of absorbed photons. The minimum is a consequence of destructive interference between the contributions of two parts of the interaction operator.
A model which describes the time evolution of strong-field photoionization of atoms is presented. Based on the numerical solution of the non-stationary Schrodinger equation, the model allows one to predict and to interpret the results of experiments on double photoionization of atoms by a combined action of a very short (attosecond) XUV pulse and a few-cycle IR pulse of a powerful laser at various delay times between the two pulses. Depending on the binding energy of the ionized electron, two types of processes are considered. If the electron is tightly bound (Ne case), the XUV pulse ionizes the atom and shakes up another (outer) electron to an excited state, which is subsequently ionized by the strong IR field. For an atom with a weakly bound outer electron (Li case), the IR field ionizes the latter, while the XUV pulse, ionizing the inner shell, terminates (or suppresses) the strong-field ionization. In both cases the yield of doubly ionized ions strongly depends on the delay time between the two pulses, revealing 'steps', oscillations and other features which characterize the time evolution of the ionization process. The presented model describes qualitatively the results of recent experiments on Ne.
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.
In the theoretical study of photoionization, certain properties of the photoelectrons are not defined in terms of any (even idealized) model for the electron-detection process, in contrast to the well-known Glauber theory of photon detection. Thus, for instance, the energy spectrum of the electron produced in atomic ionization is usually defined simply as the long-time probability for the electron to have a given energy. In this paper a formal model for an electron detector localized to a small region in space, similar to the DeWitt monopole detector, is set up in terms of which results analogous to those obtained for photon detection in the Glauber theory can be obtained. In addition, it is possible to define correlation functions describing the joint probability of detecting an electron and a photon. This correlation function is calculated here in the case of two-photon ionization of an atom modeled as having two discrete energy levels and an ionization continuum. When the atom is subjected to an incident driving field, both a photoelectron and scattered photons arising from the spontaneous decay of the upper of the two discrete levels are produced. Correlations between these photons and the photoelectron are studied here by considering the joint probability of detection of a photoelectron and a scattered photon for a monochromatic driving field.