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Physical Review A

Short-time multiphoton detachment in a one-dimensional model with very-short-range potential

Anna Sanpera, L. Roso

Published Jun 1, 1990• 15 citations
Publisher

Abstract

We study multiphoton ionization for a one-dimensional atom model (with only one bound state) solving numerically the Schr\"odinger equation. The intensity dependence of the cross section of the process is related to different ponderomotive thresholds. For very-low-intensity fields and very short times ``non-energy-conserving'' terms are dominant. The validity of perturbation theory has also been tested.

DOI
10.1103/physreva.41.6515

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We study multiphoton ionization for a one-dimensional atom model (with only one bound state) solving numerically the Schr"odinger equation. The intensity dependence of the cross section of the process is related to different ponderomotive thresholds. For very-low-intensity fields and very short times ``non-energy-conserving'' terms are dominant. The validity of perturbation theory has also been tested.
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The authors have formulated a new non-perturbative gauge-invariant analytical approach for solving the multiphoton ionization problem for a one-dimensional atomic system with a finite-range binding potential. Their method is based on the quasistationary state decay picture of ionization. They have applied the general solution to the model potential with the oscillator-like well and carried out the detailed analytical analysis of the ionization process. In the limit of moderately strong low-frequency laser fields and shallow potential wells, the authors' results reduce to those obtained for the case of an atom with the delta -well binding potential. For a finite-range binding potential one can distinguish the following peculiarities: (1) even for the case of non-resonant external field a sufficiently large number of binding states can lead to considerable changes in the multiphoton ionization; (2) in the case when the one-photon channel is open and the laser field is strong enough an atom becomes more stable as the field intensity is increased.
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).
It has been widely believed that short-pulse multiphoton ionization is dominated by a resonance process: excited states of the atom are shifted by the radiation field into multiphoton resonance with the ground state, are populated, and then rapidly ionized. A recent experiment, shows significant population remaining in excited states at the end of the laser pulse, and this result has been interpreted as indicating that ionization proceeds slowly out of these states. We investigate this issue in the framework of Floquet theory, supplemented by direct numerical solution of the time-dependent Schrodinger equation. In this framework, the standard picture is portrayed as an adiabatic transition between Floquet eigenstates, which occurs as the amplitude of the laser field is ramped through the resonance value (i.e. through an avoided crossing of Floquet quasienergies). Thus it follows that the same type of transition must occur as the field is turned off. This mechanism can yield significant populations of excited states that do not suffer appreciable ionization. We exhibit this effect by numerical studies of a model atom with two bound states and two continua.
We have studied population trapping in a one-dimensional model atom interacting with a short-pulse high-intensity laser, using Floquet analysis and direct numerical integration of the time-dependent Schrödinger equation for a range of peak pulse intensities. We find that photoelectrons are efficiently produced only by pulses whose peak intensities lie in a narrow range around the resonant intensity for a given intermediate state. Excited-state populations, however, are generated with comparable efficiencies for all pulses whose peak intensities exceed the resonant intensity. This implies that, for a realistic laser pulse with an inhomogeneous spatial distribution of intensity, excited atoms are generated throughout a larger volume than are photoelectrons. Interpretations of recent experiments are reexamined in light of this result.