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Physical Review Letters

Adiabatic and diabatic evolution in the multiphoton ionization of sodium

Dimitrios G. Papaioannou, Thomas F. Gallagher

Published Nov 30, 1992• 9 citations
Publisher

Abstract

We have measured the three photon ionization and electron energy spectra of Na from 5-ps laser pulses over the range 16 300 to 17 800 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. Together these measurements suggest that multiphoton ionization can be understood in terms of a Floquet description. Sharp discontinuities in the ionization probability and Rabi splittings in the electron energy spectra are direct consequences of adiabatic and diabatic evolution, respectively, from the initial zero-field ground state.

DOI
10.1103/physrevlett.69.3161

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We have measured the three photon ionization and electron energy spectra of Na from 5-ps laser pulses over the range 16 300 to 17 800 cm\ensuremath−1{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}cm\ensuremath−1. Together these measurements suggest that multiphoton ionization can be understood in terms of a Floquet description. Sharp discontinuities in the ionization probability and Rabi splittings in the electron energy spectra are direct consequences of adiabatic and diabatic evolution, respectively, from the initial zero-field ground state.
We have made several different types of measurements of the three-photon ionization of Li produced by 3-ps laser pulses and describe the results using a Floquet picture. Over the photon frequency range 15 000 to 15 800 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, Li represents a strongly coupled three-state system with the 2s ground state coupled to the 2p and 3d states by one and two photons, respectively. Energy analysis of the photoelectrons allows the measurement of the intensity dependent shift of the 2s Floquet state during the laser pulse. The shift shows a strong frequency dependence that is not predicted by first-order perturbation theory. We have also measured the total ionization spectrum over several ranges of frequency, as well as the angular distribution of the ionization and the first above-threshold ionization peak for frequencies where the ground state is near resonance with the 4s and 4d excited states. Calculations based on the Floquet Hamiltonian indicate that all of these processes may be understood in terms of a Floquet description.
A theoretical investigation has been carried out on the dependence of the photoelectron angular distributions on laser intensity for the case of two-photon-resonant three-photon ionization of sodium. Good overall agreement is obtained with the experimental anisotropy parameters for ionization via the 4D3/2{D}_{3/2}D3/2​ and 4D5/2{D}_{5/2}D5/2​ intermediate states. The comparison of the theoretical results with the experimental data also clearly shows that the hyperfine splitting of the ground state has to be taken into account at high laser intensities although the low-intensity angular distributions do not depend on the initial ground hyperfine state.
Two flashlamp-pumped, tunable, dye lasers have been utilized to study three-photon ionization in atomic sodium. The resulting ion yield shows large peaks at laser frequencies which correspond to electric quadrupole transitions. This is the first direct observation of electric quadrupole effects in multiphoton ionization. The $3p^{2}P_{\frac{3}{2}}\ensuremath{\rightarrow}4f$ matrix element is determined, and the fine-structure splitting of the 5p5p5p state is measured.
An experimental study of doubly resonant multiphoton ionization of Na has been carried out. Coherence effects, such as AC - Stark splitting and population trapping, have been manifested in different coupling schemes, i.e. ladder, lambda, vee configurations. These effects have been investigated in terms of their dependence on the laser intensity and resonance detuning, as well as the state of the laser polarization. The experimental results are qualitatively interpreted in terms of a few level system.
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.