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Annual Meeting Optical Society of America

Measurement of the 1S-2S two-photon Rabi frequency

Xingfu Li, Edward S. Fry

Published Jan 1, 1993• 0 citations
Publisher

Abstract

Three photon ionization enhanced by two photon resonance of the metastable 2S state of hydrogen atoms is studied with a pulsed laser at 243nm.
DOI
10.1364/oam.1993.wl.6

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Journal of Physics B Atomic Molecular and Optical Physics•Jun 23, 2008•1 citation
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 solved the time-dependent Schr\"odinger equation to analyze the time evolution of a hydrogen atom, initially in its ground 1s state, interacting with a one- or two-color linearly polarized laser pulse which is tuned close to a two-photon resonance with the 2s metastable state. The two-photon transition therefore does not involve an intermediate resonance state. Using a suitable combination of two laser pulses of different frequencies, population can be transferred from the 1s state to the 2s state via the continuum. In both the single-color and the two-color cases, a maximum amount of 17% of population can be found in the 2s state at the end of the pulse. We compare and interpret our results in terms of the time-independent Floquet eigenvalues. The system can also be modeled by an ``essential states'' two-level atom with decay. Both the Floquet and the time-dependent solutions are compared with the model predictions. The model allows systematic optimization studies for population transfer under a wide range of laser pulse parameters.
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).