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Physical Review A

Influence of the dynamic Stark effect on photoelectron angular distributions in multiphoton ionization

W. Ohnesorge, F. Diedrich, Gerd Leuchs, Daniel S. Elliott, HERBERT WALTHER

Published Mar 1, 1984• 23 citations
Publisher

Abstract

The influence of the dynamic Stark effect on photoelectron angular distributions for two-photon-resonant three-photon ionization of sodium by way of the $4^{2}D$ fine-structure components has been investigated. Owing to the dynamic Stark shift of the atomic transition frequency, the angular distributions expected at low laser intensities were modified as different transitions were intensity tuned into and out of resonance with the laser frequency. The distributions are in good qualitative agreement with theory.

DOI
10.1103/physreva.29.1181

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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.
In this paper, we present the theory of photoelectron angular distributions in resonant multiphoton ionization that rigorously takes into account the saturation, ac Stark-shift, and the laser-linewidth effects. The influence of these effects on the distribution is incorporated through the coupling equations between the angle-resolved ionization probabilities and the (time-dependent) bound-state density-matrix elements. General expressions for the angular distributions are derived and several properties of these distributions are arrived at from these expressions. Finally, numerical results are presented to illustrate the effects of saturation, of ac Stark shifts, and of the laser line shape.
The energy levels of atoms and molecules exposed to intense, short, high-frequency laser pulses undergo time-dependent distortion known as dynamic Stark shift (DSS). These level shifts are induced by the coupling with nonresonant (nonessential) states and follow the temporal intensity profile of the laser pulse. Owing to the different DSSs of the individual atomic levels, transient resonance suppressions and enhancements significantly modify the multiphoton ionization pathway, leaving clear fingerprints (asymmetry, splitting, and shifting) in the energy spectrum of emitted photoelectrons. Here we investigate this phenomenon by solving the time-dependent Schr\"odinger equation of the valence electron of Na and Li in increasing levels of complexity: (i) developing minimal models for two-photon transition and (2+12+12+1)-photon ionization, (ii) applying a spectral method without continuum-continuum couplings, and (iii) propagating the electron wave packet on a large spatial grid accounting for all possible couplings. We show that appropriately detuned transform limited pulses provide a high level of control in strong-field excitation, when the atomic levels are dynamically shifted. Furthermore, we demonstrate the role of DSSs in the multipeak structure of the Autler-Townes doublet, found when several Rabi oscillations are induced during the strong-field resonant ionization.
The influence of the ac-Stark shifts on the spin polarization (SP) of the photoelectron in a resonant multiphoton ionization is discussed. It is shown that the Stark shifts of various levels are different and this removes any initial fine-structure degeneracy of the excited states. This increased dynamic separation between the states increases the SP of the ejected photoelectron. Numerical results are presented to illustrate this effect. By expressing the equations of motion in the spin basis set the precise conditions necessary to observe nonzero SP are identified. It is shown on the basis of these conditions that although the removal of the fine-structure degeneracy occurs independent of whether the atom has any spin-orbit coupling, this does not induce any spin polarization if the atom has no spin-orbit coupling.