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Physical Review Letters

Saturation of Resonant Two-Photon Transitions in Thallium Vapor

Charles C. Wang, Leighton I. Davis

Published Sep 8, 1975• 56 citations
Publisher

Abstract

We present direct evidence on the saturation of resonant two-photon transitions in the optical region. Saturation manifests itself as a broadening of the transition linewidth and as a deviation from the low-level intensity dependence for both third-harmonic generation and two-photon-induced fluorescence. These effects may greatly limit the extent of attainable resonant enhancement in experiments which require high intensity for excitation.

DOI
10.1103/physrevlett.35.650

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Journal of Physics B Atomic and Molecular Physics•Feb 14, 1985•2 citations
We present direct evidence on the saturation of resonant two-photon transitions in the optical region. Saturation manifests itself as a broadening of the transition linewidth and as a deviation from the low-level intensity dependence for both third-harmonic generation and two-photon-induced fluorescence. These effects may greatly limit the extent of attainable resonant enhancement in experiments which require high intensity for excitation.
We have observed fluorescence and ionization signals resulting from two-photon resonant excitation of thallium in an atomic beam. The output of a pulsed dye laser is used to excite the resonance between the ground state (6('2)P(,1/2)) and an excited n('2)P state of thallium. Both two-photon absorption and three-photon absorption occur simultaneously; the latter results in photoionization of the atom. The excited states populated by two-photon absorption decay via cascade fluorescence back to the ground state; one or more of these spectral components constitute our fluorescence signal. The lifetimes of the excited n('2)P states of thallium have been measured directly by observing the exponential decay of this fluorescence. Calculations are included to ascertain the time required for the fluorescence signal to reach within 2% of a simple exponential decay. This decay is a measure of the lifetime of the initial state, under the condition that none of the fluorescence components arise from states which are populated by cascade through longer-lived states. The lifetimes of the n('2)P(,1/2) and n('2)P(,3/2) states of thallium for n = 7 to 11 are determined in this manner and compared with the values deduced from semi-empirical calculations of oscillator strengths by various authors. For calculations employing the effects of core polarizability in the electron wavefunctions and in the transition matrix elements, the agreement is very good--to within our experimental uncertainty, which is typically(, )<5%. Our measurements are also compared to the four other known experimental values for such excited states of thallium. Some of these previous experiments and calculations were carried out in conjunction with parity non-conservation experiments in thallium. Our measurements may provide useful checks on the accuracy of some of the calculations performed in the evaluation of such experiments. The ionization and fluorescence signals are also studied under conditions of strong saturation of the two-photon resonance with the 7('2)P states. The manifestation of saturation in the ionization signal is a broadening of the excitation spectrum, which is found to greatly exceed that of the fluorescence signal. Furthermore, the ratio of the ionization signal to the fluorescence signal at the peak of the resonance is found to vary linearly at intensities below about 10('9) W/cm('2); this too saturates at higher intensities. Various models are employed to simulate the observed behavior, encompassing both rate equations as well as density matrix formulations. The numerical solutions to these models are compared with the observed behavior; the agreement is found to depend strongly on the assumed experi- mental conditions to which the ensemble of atoms is subjected.
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.
Resonant enhancement of optical third-harmonic generation in cesium vapor has been observed when twice the energy of the fundamental photon becomes equal to the energy difference between the 9d2D329d^{2}D_{\frac{3}{2}}9d2D23​​ level and the ground state of the cesium atom. The measured, effective coefficient is ${10}^{\ensuremath{-}30}$ esu/atom, which is more than a factor 108{10}^{8}108 larger than the corresponding coefficient for the helium atom. An effective coefficient is synthesized by first calculating the coefficient for a single cesium atom at rest and then including the effects of Doppler broadening and the fundamental laser spectrum. The calculated value is in satisfactory agreement with experiment.
The light statistical dependence of stationary saturated two-photon transitions is discussed. While at low intensities, in comparison with light having a stable amplitude, Gaussian amplitude fluctuations of the exciting radiation are more effective in populating the excited resonant state, light with amplitude fluctuations is less effective in saturating a two-photon transition. The amplitude fluctuations are shown to wash out the resonance curves. While at low intensities the effective Stark shift (i.e. the maximum of the dispersion curve) is larger by a factor of three in light with Gaussian amplitude fluctuations compared with radiation of constant amplitude, this enhancement factor becomes intensity dependent with increasing intensity.