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Physical Review Letters

Rate Theory for the Four-Photon Ionization of Cs near the 6F Resonance

Burke Ritchie

Published Nov 5, 1979• 5 citations
Publisher

Abstract

A previously presented narrow-bandwidth theory is used to interpret recent data on the four-photon ionization of Cs near the $6F$ resonance. The theory is based on treating the amplitude of the radiation field as a constant relative to its rapid phase oscillations. The ionization rate adiabatically follows a pulsed amplitude leading to maximum ionization for times at which the pulse develops sufficient intensity to shift the $6S\ensuremath{\rightarrow}6F$ transition into resonance.

DOI
10.1103/physrevlett.43.1380

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A previously presented narrow-bandwidth theory is used to interpret recent data on the four-photon ionization of Cs near the 6F6F6F resonance. The theory is based on treating the amplitude of the radiation field as a constant relative to its rapid phase oscillations. The ionization rate adiabatically follows a pulsed amplitude leading to maximum ionization for times at which the pulse develops sufficient intensity to shift the 6S\ensuremath→6F6S\ensuremath{\rightarrow}6F6S\ensuremath→6F transition into resonance.
The author presents a theory for NNN-photon ionization in which two intermediate states can be in resonance with the ground state over a narrow range of photon frequencies. The theory is applied to the three-photon 6F6F6F resonance-state spin-orbit doublet in the four-photon ionization of Cs. The amplitude for the process is the sum of two components, each containing a complex line-shape function. In the limit of zero splitting, the previously studied isolated resonance result, in which the line shape is Lorentzian is recovered. For the splitting in Cs (6F6F6F), the absorption profile is studied as a function of the splitting parameters of the state, the $6S\ensuremath{\rightarrow}6F$ three-photon Rabi rate, and the field-induced shift and width for the $6S\ensuremath{\rightarrow}6F$ transition. This profile depends in a complicated way on the relative magnitudes of the shift and the spacing between the fine-structure levels.
Presents the first application to a physical case of the effective-operators method introduced by Armstrong, Beers and Feneuille (1975) to interpret resonant multiphoton ionisation. In particular, the four-photon ionisation of Cs I near the 6f resonance is considered. Atomic quantities needed for the evaluation of effective operators are obtained by using a non-relativistic central-potential model. Theoretical results are compared with experimental data recently obtained by Morellec, Normand and Petite (1976). Taking into account the uncertainty of the measurements, the main experimental features and, in particular, the shapes of the resonance curves are reproduced well by the calculation described here.
This paper reports the four-photon ionization of caesium atoms when the laser frequency is tuned through the resonant three-photon transition 6S → 6F. This experiment was performed by using a tunable-wavelength bandwidth-limited subnanosecond laser pulse at 1.06 μm, in the 108-109 W.cm-2 laser intensity range. Pulse widths of 1.5 ns, 50 ps, and 15 ps were used. The resonant character of the multiphoton ionization process was observed, even with the shortest pulse of 15 ps. Nevertheless the influence of a temporal effect is demonstrated according to theoretical predictions. The resonance shift ΔE of the 6S → 6F transition energy was found to be linear with the laser intensity I within the range 108-109 W.cm-2. ΔE = α I, with α = 2 cm-1/GW.cm-2. This result confirms previous measurements performed with single-mode 35 ns laser pulses and is in very good agreement with calculated resonance shifts.
The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order 108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2) is determined by the intensity-dependent level width (6f6f6f configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order 1012{10}^{12}1012 W/cm2{\mathrm{cm}}^{2}cm2) are determined by both the intensity-dependent widths and shifts as‘\stackrel{\mathrm{`}}{\mathrm{s}}s‘ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.
We present a theoretical study of doubly resonant three-photon ionization with radiation of sufficiently broad bandwidth to overlap all hyperfine levels of the resonant intermediate states. We demonstrate that isotopic selectivity in ionization is apt to occur under a variety of circumstances, although the degree may vary from negligible to quite significant, depending on the relative values of atomic and radiation parameters. Our theory provides a satisfactory quantitative interpretation of recent experimental data in Sn.