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Modern Physics Letters B

THE ROLE OF RESONANCES IN MULTIPHOTON IONIZATION OF ATOMS WITH SHORT INTENSE LASER PULSES

Rutger B. Vrijen, J. H. Hoogenraad, Lambertus D. Noordam

Published Feb 20, 1994• 4 citations
Publisher

Abstract

We present experimental and theoretical data on the electron energy spectra from resonance-enhanced multiphoton ionization of atoms. In experiments performed with 594-nm wavelength, linearly polarized laser pulses of 300-fs and 600-fs durations, it is found that excitation of the intermediate resonances during the rising edge of the laser pulse can dominate the electron spectrum. Good agreement is found between the experimental results and a model based on the Landau-Zener energy level crossing theory. Theoretical results obtained with direct integration of the Schrödinger equation show that intermediate resonances can be excited appreciably off resonance if the coupling between the ground state and the excited state is highly nonlinear. The excitation of the intermediate state is not localized at the intensity which makes it six-photon resonant with the ground state. A multilevel model used to simulate the experimental spectra, based on direct integration of the Schrödinger equation, shows excellent agreement with the data.

DOI
10.1142/s0217984994000224

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We present experimental and theoretical data on the electron energy spectra from resonance-enhanced multiphoton ionization of atoms. In experiments performed with 594-nm wavelength, linearly polarized laser pulses of 300-fs and 600-fs durations, it is found that excitation of the intermediate resonances during the rising edge of the laser pulse can dominate the electron spectrum. Good agreement is found between the experimental results and a model based on the Landau-Zener energy level crossing theory. Theoretical results obtained with direct integration of the Schrödinger equation show that intermediate resonances can be excited appreciably off resonance if the coupling between the ground state and the excited state is highly nonlinear. The excitation of the intermediate state is not localized at the intensity which makes it six-photon resonant with the ground state. A multilevel model used to simulate the experimental spectra, based on direct integration of the Schrödinger equation, shows excellent agreement with the data.
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.
When exposed to intense light of \ensuremath{\sim}580 nm, the ground state of K shifts up in energy, passing through two-photon resonances with Rydberg states and finally crossing the two-photon ionization limit. Using laser pulses of 0.5 to 13 ps duration, we have shown experimentally that ionization occurs for short pulses, but for long pulses the population is diverted into the Rydberg states where some population survives the peak intensity of the pulse, in excellent agreement with a dynamic Floquet model.
We have studied two-photon resonant three-photon ionization of atomic sodium vapor. A dye laser tuned to either the 4d or 5s two-photon allowed transition was used to excite the atom and a second more intense laser (λ = 7000 Å) was used for ionization. The ion yield was measured as a function of resonant laser intensity and detuning, the nonresonant laser intensity, and the temporal overlap of the exciting and ionizing laser pulses. We have found1 that at high laser intensities the photoionization yield decreases as the nonresonant laser intensity is increased. When tuned to the 5s level a value of ~−0.6 was obtained for the exponential index even with the resonant laser tuned to maximize the ion yield. A theoretical model including the effects of Stark shift of the ground state, power broadening of the intermediate level due to saturation of the two-photon transition and by rapid transitions to the ionization continuum was used to predict the experimental results. Good agreement between theory and experiment required the use of a photoionization cross section for the 5s level which was ~20 times greater than the accepted value. Results for photoionization from the 4d level are also presented.
The non linear interaction between an intense laser radiation and atoms leads to ionization through the absorption of N photons from the laser radiation via laser-induced virtual states. The multiphoton ionization rate varies as a function of the laser intensity I as IN. We discuss the two most important effects which govern multiphoton ionization processes : resonance effects and laser-coherence effects. In a moderate laser intensity range (107 - 109 W cm-2) corresponding to the two, three or four-photon ionization of atoms, resonance effects play a dominant role while the photon statistics of the laser radiation are relatively unimportant. On the contrary, in the very high intensity range (1012 - 1013 W cm-2) required to observe large Nth - order ionization processes, coherence effects play a dominant role through N! enhancement in the N-photon ionization rate, while resonance effects are completely damped due to the high laser intensity. We conclude by reviewing the possible applications of multiphoton absorption processes in other fields.
We present a theoretical analysis of multiphoton ionization through resonant intermediate states shifted through resonance during a short, intense pulse. The resonant structure in the photoelectron spectra is compared with what it would be if the peak intensity or the frequency of the laser were scanned, and the various differences are discussed in detail. The dynamical behavior is described in terms of a density matrix evolving under a realistic temporal and spatial pulse shape. Our results, on atoms with realistic parameters, show structure similar to that observed in recent experiments. Results for circularly polarized light are also presented. The limitations and advantages of the model are discussed.
The resonant multiphoton resonances shifts and widths and ionization cross-sections for multielectron atoms in a intense laser radiation field are studied. It is carried out a new consistent approach to atom in a strong realistic laser field, based on the relativistic energy formalism (S-matrix adiabatic formalism), relativistic Dirac equation Green function method and relativistic many-body perturbation theory with the Dirac-Kohn-Sham zeroth approximation. In relativistic theory, the Gell-Mann and Low adiabatic formula for energy shift is connected with electrodynamical scattering matrice, which includes interaction with as a laser field as a photon vacuum field (radiative decay). The optimized basis of the relativistic orbitals is generated with using a minimization procedure for the gauge-non-invariant contribution (the fourth-order of the QED perturbation theory) to the radiation width of atomic state. An approach to treating the multiphoton atomic processes is outlined on example of H, Cs, Kr,Mg etc. Analysis shows that the shift and width of the multi-photon resonance line for the interaction “atom- multimode laser pulse” is greater than the corresponding shift and width for a case of the “atom- single-mode pulse” (the Lorenz pulse model) interaction. From the physical point of view it is naturally provided by action of the photon-correlation effects and influence of the laser pulse multi-modity.