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Annual Meeting Optical Society of America

The 1S → 2S two-photon transition rate in atomic hydrogen

Shifang Li, Edward S. Fry

Published Jan 1, 1991• 0 citations
Publisher

Abstract

Theoretical calculations for the 1S → 2S two- photon transition rate in atomic hydrogen are reviewed. They are compared with two experiments via the saturation effects that are observed when three-photon ionization is enhanced by two- photon resonance with the metastable 2S state. There is a significant disagreement between theoretical and experimental results. The disagreement is illustrated by determining the transition rate as a function of intensity for experimental laser profiles: (1) using parameters that give rates in agreement with experimental data, and (2) using theoretical values for the parameters. Finally, experiments that would involve direct observation of the 2S metastable state are considered. It is shown that single-longitudinal-mode laser experiments would provide an accurate measurement of the Rabi frequency for this transition and yield a definitive value for the rate. A Monte Carlo simulation method is used to consider practical effects associated with such an experiment, for example, chirp and ASE noise in the laser. Also, simulations of the multiphoton ionization process in multimode and wide band laser fields are presented.

DOI
10.1364/oam.1991.we5

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Annual Meeting Optical Society of America•Jan 1, 1993•0 citations
Theoretical calculations for the 1S → 2S two- photon transition rate in atomic hydrogen are reviewed. They are compared with two experiments via the saturation effects that are observed when three-photon ionization is enhanced by two- photon resonance with the metastable 2S state. There is a significant disagreement between theoretical and experimental results. The disagreement is illustrated by determining the transition rate as a function of intensity for experimental laser profiles: (1) using parameters that give rates in agreement with experimental data, and (2) using theoretical values for the parameters. Finally, experiments that would involve direct observation of the 2S metastable state are considered. It is shown that single-longitudinal-mode laser experiments would provide an accurate measurement of the Rabi frequency for this transition and yield a definitive value for the rate. A Monte Carlo simulation method is used to consider practical effects associated with such an experiment, for example, chirp and ASE noise in the laser. Also, simulations of the multiphoton ionization process in multimode and wide band laser fields are presented.
We have measured the resonance-enhanced four-photon ionization of atomic hydrogen. The degenerate four-photon process occurs via a three-photon resonance between the 1s and the 2p levels, with subsequent one-photon ionization near threshold. We have studied the highly asymmetric resonance-enhanced profile, i.e., the photoion yield as a function of laser detuning from three-photon resonance between the 1s and 2p levels. In particular, we have determined the width, shift, peak, and asymmetry of the profile as a function of laser intensity. The experimental results are compared to theoretical models. These models involve both the properties of the atom in an intense near-resonant radiative field, and a detailed model for the multimode laser field, particularly the field fluctuations due to mode beating. The asymmetric resonance-enhanced photoionization profile is well reproduced by both a random-phase and a chaotic-light model.
The two-level model of multiphoton ionization is reviewed within the context of an exact theoretical framework. Parametrization of the complex dressed states arising in a generalized Floquet analysis gives numerical values for the effective two-level parameters for two-, three-, and four-photon ionization of ground-state atomic hydrogen with the (ml=0{m}_{l}=0ml​=0) intermediate resonant states 2p2p2p, 2s2s2s, and 3p3p3p, respectively. Detailed time dependences of the ionization process are given for responses to a linearly polarized, monochromatic, single-mode laser turned on suddenly with respect to near-resonant states, but adiabatically with respect to all others. Appropriate expressions for time-independent ionization rates are obtained during specific time intervals. The KKK index ($K=\frac{\ensuremath{\partial}\mathrm{ln}N}{\ensuremath{\partial}\mathrm{ln}I}$), of interest in recent experiments, is understood within the framework of a simple model. Application to four-photon ionization of the metastable 2S12^{2}S_{\frac{1}{2}}2S21​​ state of hydrogen illustrates the breakdown of the two-level model, as the number of "near-resonant" levels is a function of the field strength.
Analyses of the resonant multiphoton ionization of atoms require knowledge of ac Stark energy shifts and of multiphoton, bound-to-bound state, transition amplitudes. In this paper, we consider the three-photon photoionization of hydrogen atoms at frequencies that are at and surrounding the two-photon 1s to 2s resonance. AC energy shift sums of both the 1s and 2s states are calculated as a function of the laser frequency along with two-photon 1s ? 2s resonant transition amplitude sums. These quantities are calculated using an extended version of a method, which has often been employed in a variety of ways, of calculating these sums by expressing them in terms of solutions to a variety of differential equations that are derived from the different sums being evaluated. We demonstrate how exact solutions are obtained to these differential equations, which lead to exact evaluations of the corresponding sums. A variety of different cases are analysed, some involving analytic continuation, some involving real number analysis and some involving complex number analysis. A dc Stark sum calculation of the 2s state is carried out to illustrate the case where analytic continuation, pole isolation and pole subtraction are required and where the calculation can be carried out analytically; the 2s state, ac Stark shift sum calculations involve a case where no analytic continuation is required, but where the solution to the differential equation produces complex numbers owing to the finite photoionization lifetime of the 2s state. Results from these calculations are then used to calculate three-photon ionization probabilities of relevance to an analysis of the multiphoton ionization data published by Kyrala and Nichols (1991 Phys. Rev. A 44, R1450).
The two-photon transition rate for hydrogen is evaluated with the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}}$ and the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ interactions including the continuum. We find that the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}}$ interaction approaches the final result with a small number of intermediate states and consequently is the one to be used in any approximate calculation. Numerical values of the two-photon absorption coefficient as a function of frequency are given and the resonance enhancement is exhibited.