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Journal of Physics B Atomic and Molecular Physics

Resonant multiphoton ionisation with intense monochromatic lasers

S. Geltman

Published Jan 14, 1980• 19 citations
Publisher

Abstract

A theoretical procedure is presented for the evaluation of resonant multiphoton ionisation rates for atoms interacting with intense monochromatic lasers. The essence of the procedure is to treat first the strong coupling by solution of the truncated Schrodinger equation to obtain a time-dependent superposition state. This is then used as the lowest order approximation to iterate the full time-dependent Schrodinger equation to obtain the transition amplitude to the continuum. A model-atom study of the time evolution of the ionisation probability is carried out and the approach to rate behaviour in the long-time limit is demonstrated. Ionisation rates are evaluated for a variety of resonant processes in H, Na and Cs involving one or two lasers, as a function of intensities and detunings. Comparison with experiment is still in a fragmentary stage, and some large discrepancies are found to exist.

DOI
10.1088/0022-3700/13/1/018

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Australian Journal of Physics•Oct 1, 1995•0 citations
A theoretical procedure is presented for the evaluation of resonant multiphoton ionisation rates for atoms interacting with intense monochromatic lasers. The essence of the procedure is to treat first the strong coupling by solution of the truncated Schrodinger equation to obtain a time-dependent superposition state. This is then used as the lowest order approximation to iterate the full time-dependent Schrodinger equation to obtain the transition amplitude to the continuum. A model-atom study of the time evolution of the ionisation probability is carried out and the approach to rate behaviour in the long-time limit is demonstrated. Ionisation rates are evaluated for a variety of resonant processes in H, Na and Cs involving one or two lasers, as a function of intensities and detunings. Comparison with experiment is still in a fragmentary stage, and some large discrepancies are found to exist.
The time evolution of the ionisation probability of a sodium atom irradiated by linearly polarised light with frequency near the 3s-3p transition frequency is studied theoretically by the following method. The 3s and 3p states are strongly coupled using the rotating-wave approximation and then the resulting strongly coupled wavefunction is used as the lowest-order approximation in applying second-order perturbation theory to obtain the ionisation probability. The photoelectron energy spectrum and total ionisation probability are studied for various laser detunings and turn-on forms. Processes which are forbidden at long times by energy conservation are found to be important at short times (t<or approximately=10 -9 s for a laser intensity of order MW cm -2 ) . The ionisation probability is found to exhibit a plateau behaviour at times much less than the 3s-3p Rabi cycling time and subsequently to oscillate with the 3p population before reaching rate behaviour in the long-time limit.
The authors treat a model for photoionisation in which the atom has many bound atomic levels and the laser may be either monochromatic or possess a finite bandwidth. The treatment is restricted to the case where the laser is not sufficiently intense to cause Stark splitting of the atomic energy levels. They obtain an expression for the two-photon ionisation probability as a function of time which covers both resonant and non-resonant excitation. They identify several time regimes where the probability takes on a particularly simple form. In particular they discuss the short time behaviour and the conditions under which a time-independent transition rate exists. Numerical plots of the ionisation probability against laser frequency for a wide range of pulse durations are given for the two-level model.
A rigorous and practical time-dependent formulation of quantum decay processes is obtained by converting the Hermitian Schrodinger problem into an equivalent non-Hermitian Schrodinger equation. The properties of the original Hermitian and the reduced non-Hermitian Hamiltonians are compared and the non-Hermitian formulation is shown to be consistent with the theorem of Fock and Krylov for the description of truly decaying states. A self-consistent non-unitary algorithm is developed and used to obtain expressions for the time-dependent transition amplitudes of interest; they automatically preserve the total probability in the sum space at all future times tau >0. The formalism is coded for application to the important problem of ionisation decay of a ground-state hydrogen atom coupled to a strong radiation field with a sub-threshold photon frequency. The first quantitative information on the time dependence of two- and three-photon (resonant and non-resonant) ionisation of the hydrogen atom is obtained.
Two-laser multiphoton ionisation under the autoionising-like resonance condition is studied theoretically within an extended atomic model dictated by the experiment of Feldmann et al (1986). Ordinary coupling between a selected pair of bound states via the continuum only is supplemented in the author's model by Raman-type coupling involving the atomic spectrum below the ionisation threshold. In the case considered this additional Raman coupling enhances the ionisation rate to a much greater extent than the coupling via the continuum can do. The Raman coupling modifies the autoionising-like shape parameter and is decisive as far as the resonance peak profile is concerned. Exploiting this Raman coupling within the atomic model with four effective bound states, the author gives explanations for all the details of the ionisation spectrum detected by Feldmann et al, i.e. the number of resonance peaks, their strength, fine structure, shape, relative heights and sensitivity to the laser field.
Perturbation theory of multiphoton ionisation due to a classical electromagnetic field is modified to allow for intermediate resonances with bound states. Complex energies, generally associated with resonances, do not enter into this formalism. For a monochromatic field of frequency u, a constant ionisation rate can then be defined unambiguously and only such continuum states are excited which correspond to the absorption of energy in integral multiples of hu. As an application, differential and total cross sections for the two-photon ionisation of hydrogen, for frequencies below the n = 3 resonance region, are obtained in closed form. Existing data for generalised cross sections, calculated numerically using the complex coordinate method, are in good agreement with the present results. Finally, the mean fractional ionisation resulting from a pulse of finite duration is estimated on the basis of the associated power spectrum. For short pulses, the time dependence of ionisation exhibits a departure from that expected of a time-independent rate.