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Journal of Physics B Atomic Molecular and Optical Physics

Photoionization of the hydrogen atom in an intense high-frequency field: the two-pole approximation

R. Lefèbvre, B. Stern, Osman Atabek

Published Jan 1, 1999• 2 citations
Publisher

Abstract

High-frequency Floquet theory (HFFT) is again applied to photoionization in a linearly polarized field of the hydrogen atom in its ground state. The new feature is the systematic use of a two-pole approximation to represent both the dressed potential (with two positive charges) and the coupling responsible for one-photon ionization (with two charges of opposite sign). Within such a scheme, both the initial bound and the final continuum states can be very accurately determined. The final continuum state is obtained by deriving, from Floquet theory, an equation involving a source term. The model accounts reasonably well, even at rather low frequencies, for the stabilization of the atom in an intense field and supports the claim that HFFT represents the photoionization rate with a golden rule expression involving dressed states.

DOI
10.1088/0953-4075/32/13/315

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High-frequency Floquet theory (HFFT) is again applied to photoionization in a linearly polarized field of the hydrogen atom in its ground state. The new feature is the systematic use of a two-pole approximation to represent both the dressed potential (with two positive charges) and the coupling responsible for one-photon ionization (with two charges of opposite sign). Within such a scheme, both the initial bound and the final continuum states can be very accurately determined. The final continuum state is obtained by deriving, from Floquet theory, an equation involving a source term. The model accounts reasonably well, even at rather low frequencies, for the stabilization of the atom in an intense field and supports the claim that HFFT represents the photoionization rate with a golden rule expression involving dressed states.
The high-frequency Floquet theory (HFFT) of laser-atom interactions solves the space-translated version of the Schr\"odinger equation by an iterative procedure, leading to corrections of increasing order in the inverse photon energy. The lowest-order approximation (high-frequency limit) has been often evaluated before, but its accuracy at finite frequencies has not been established. To explore this issue we have computed the corrections yielded by the first-order iteration to the energy levels, and the ionization rates of a one-dimensional atomic model with a Gauss attractive potential. We have then compared, at frequencies above the field-free ionization potential \ensuremath{\Vert}W0{\mathit{W}}_{0}W0​\ensuremath{\Vert}, the HFFT results with those of a full Floquet calculation. We show that the agreement is substantially improved by the inclusion of the HFFT corrective terms. The agreement is good at all intensities for photon energies larger than several times \ensuremath{\Vert}W0{\mathit{W}}_{0}W0​\ensuremath{\Vert}. Even when the photon energy is marginally larger than \ensuremath{\Vert}W0{\mathit{W}}_{0}W0​\ensuremath{\Vert} the discrepancies vanish at sufficiently high intensities. \textcopyright{} 1996 The American Physical Society.
We formulate a computationally feasible method for calculating multiphoton ionization rates for atoms exposed to intense fields in the intensity regime where perturbation theory ceases to apply. The method is based on the time-independent picture of ionization, which starts with the Floquet ansatz. The question of the gauge of the radiation field is discussed in some detail. Various expressions for the ionization amplitude are derived from a variational principle, with the radiation field expressed in the velocity gauge. We consider in particular an approximation in which the wave vector developing from the initial state is replaced by a trial vector that is the Floquet expansion truncated just below the threshold for ionization, and in which the wave vector developing into the final state is replaced by a trial vector that is just the wave vector appearing in the Kroll-Watson low-frequency approximation in scattering theory. We have applied this approximation to hydrogen and we present some results for both nonresonant and resonant multiphoton ionization. We argue that the experimentally observed resonance structure in the above-threshold peaks of the ionization signal occurs through the electron jumping from one dressed-state energy-eigenvalue curve to another.
The strong-field multiphoton ionization of atoms is considered and a theoretical approach dealing nonperturbatively with the radiation field formulated. The general computational scheme is the conventional perturbation theory, but the intermediate states are dressed by the field. We present in detail a method to dress the continuum states and to study the dipole transitions within the continuum. In the high-frequency domain, the proposed procedure rapidly converges over a wide range of field intensity and offers an interesting framework for calculating ionization rates for arbitrary numbers of absorbed (above-threshold) photons and field polarization.
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.
We calculate the two-color ionization profile of atomic hydrogen in the presence of both a weak tunable high-frequency laser field and a low-frequency laser field of moderate intensity. The high-frequency spectroscopic light is used to probe the structure of Rydberg states dressed by the low-frequency field. We construct the photoionization spectrum from the sum of the resonance contributions by calculating the transition dipole moments between the initial state and the dressed Rydberg states, analogous to the study of photoionization in the presence of a dc field carried out by Alvarez and Silverstone [Phys. Rev. Lett. 63, 1364 (1989)].