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Journal of the Optical Society of America B

Theoretical aspects of three-photon two-color ionization of xenon through ac-Stark-shifted resonant Rydberg states

Anne L’Huillier, X. Tang, P. Lambropoulos, Louis A. Lompre, Didier Normand

Published Oct 1, 1989• 29 citations
Publisher

Abstract

We present a theoretical analysis of a recent experiment [ J. Opt. Soc. Am. B6, 1513 ( 1989)] on two-color three-photon ionization of Xe through resonant even-parity Rydberg states. We calculate second-order ac-Stark shifts, two-photon Rabi frequencies, and ionization widths by using wave functions obtained from a multichannel quantum-defect-theory analysis of the Rydberg series in Xe. We perform a detailed description of the experiment, using the density-matrix formalism, accounting for the temporal and spatial distributions of the laser fields. The agreement with the experiment is good except for the ac-Stark shift of the Rydberg states, which, in our calculation is close to the ponderomotive energy, whereas in the experiment it is measured to be half of this value.

DOI
10.1364/josab.6.001790

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Physical Review A•Oct 1, 1984•8 citations
We present a theoretical analysis of a recent experiment [ J. Opt. Soc. Am. B6, 1513 ( 1989)] on two-color three-photon ionization of Xe through resonant even-parity Rydberg states. We calculate second-order ac-Stark shifts, two-photon Rabi frequencies, and ionization widths by using wave functions obtained from a multichannel quantum-defect-theory analysis of the Rydberg series in Xe. We perform a detailed description of the experiment, using the density-matrix formalism, accounting for the temporal and spatial distributions of the laser fields. The agreement with the experiment is good except for the ac-Stark shift of the Rydberg states, which, in our calculation is close to the ponderomotive energy, whereas in the experiment it is measured to be half of this value.
Nonresonant ac Stark shifts of Rydberg states in Xe have been investigated by probing an atomic transition with a weak UV light in the presence of an intense YAG-laser pulse. Rydberg atoms produced through two-photon excitation, 5p → np (n = 15–48) and 5p → nf (n = 12–49), are subsequently ionized. IR-laser-induced shifts of the resonant ionization profiles are then measured. The measured shift, 3.9 ± 0.3 cm−1 at 1010 W cm−2, is more than a factor of 2 smaller than that expected from the basis of ponderomotive term, 8.5 cm−1 at 1010 W cm−2. In addition, the shift varies linearly as a function of the IR-laser intensity and does not depend on the principal quantum number of the np and nf series investigated here.
The Stark spectra of autoionizing Rydberg states of Xe converging to the second ionization limit 5p5{p}^{5}p5 2P1/2^{2}P_{1/2}2P1/2​ have been investigated as a function of applied electric field over the range 26--2362 V/cm. Single-photon excitation from the Xe ground state was achieved using coherent radiation near 92.5 nm, generated by frequency tripling the pulsed output of a frequency-doubled dye laser in a free jet of rare-gas atoms. For the lowest electric field only the ns' and nd' series were observed. As the electric field was increased the np' series appeared because of the mixing of wave functions with different l values. Further increase of the electric field caused the appearance of hydrogenlike Stark manifolds. The Stark spectrum was simulated in a two-step procedure with no adjustable parameters. Using a jl-coupling basis set the Hamiltonian matrix was diagonalized to determine the energy levels and corresponding eigenfunctions for a given electric field strength. The intensities and line shapes were then calculated using the formalism developed by Fano for a many-discrete-level--single-continuum configuration interaction. This treatment was sufficient to reproduce the positions, widths, and shapes of most observed features. At field strengths between 1000 and 2000 V/cm, however, an additional modulation structure with a spacing of about 2.7 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ appeared on top of the \ensuremath{\Vert}M\ensuremath{\Vert}=1 autoionizing resonances, which could not be explained by our simple theoretical model.
An electron spectroscopic study is reported of multiphoton ionisation of Xe and Cs using two laser beams. One of the two beams is tuned to multiphoton resonance with an intermediate state and causes a considerable AC Stark shift. The second beam acts as a probe of the population and shift of the intermediate state. In Xe the authors deal with a three-photon resonance with the 6s level ( lambda approximately=440 nm); in Cs with two-photon resonances with Rydberg levels of the nd series. As probes, beams of either lambda =1064 or 532 nm have been used.
The influence of ac Stark shifts on the three-photon ionization of cesium in a moderate-intensity laser beam is investigated. The ionization process involves a two-photon resonance with the 8d8d8d fine-structure levels. The work consists of two related parts. In the first part, atomic parameters, such as the two-photon Rabi rate and the ac Stark shift, are calculated in the nonrelativistic Hartree-Fock approximation. In the second part, the atomic parameters thus obtained are used as coefficients in a system of coupled differential equations representing the time evolution of the density matrix. Ionization line shapes are generated for a transform-limited pulsed laser of moderate intensity with a single-mode transverse structure. As the time history of the intensity profile is varied from square to smooth, the ionization line shape becomes asymmetric due to the time dependence of the ac Stark shift. The effects of varying the spatial intensity distribution of the laser light to include transverse centering and longitudinal focusing are also studied.