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Soviet Journal of Quantum Electronics

Profile of the two-photon absorption line due to the 1S-2S transition in atomic hydrogen

E. V. Baklanov, V. P. Chebotaev

Published Mar 31, 1975• 1 citation
Publisher

Abstract

An analysis is made of the profile of a two-photon absorption line of hydrogen free of the first-order Doppler broadening. The possibility of eliminating the quadratic Doppler effect with the aid of a narrow peak of the second derivative of the line profile is considered. It is shown that for a realistic temperature stability it should be possible to achieve a reproducibility of the order of 10 −15 .

DOI
10.1070/qe1975v005n03abeh011018

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An analysis is made of the profile of a two-photon absorption line of hydrogen free of the first-order Doppler broadening. The possibility of eliminating the quadratic Doppler effect with the aid of a narrow peak of the second derivative of the line profile is considered. It is shown that for a realistic temperature stability it should be possible to achieve a reproducibility of the order of 10 −15 .
The profile of a two-photon resonant absorption line of a particle subjected to a standing optical wave is calculated allowing for the quadratic Doppler effect. It is shown that the line profile is governed entirely by the ratio of the homogeneous line width to the quadratic Doppler frequency shift. An exact expression is obtained for the line profile in the second order in ν/c and the main approximations are considered. The profiles are calculated for the 1S-2S and 1S-3S transitions in the hydrogen atom.
The problem of two-photon interaction of atoms with the field of two standing-wave pulses is solved. It is shown that the transit broadening of the line caused by a finite pulse duration and finite transit time of atoms through the light beam is eliminated. On focusing the field a transverse velocity selection of atoms occurs that lends to a decrease of the quadratic Doppler shift of the frequency. A new value of the amplitude of the induced 1S--2S two-photon transition of hydration is obtained that is used for the calculation of the signals. The resonance amplitude in hydrogen proves to be larger for existing pulsed radiation sources than that in continuous excitation by the field.
The high resolution two-photon spectroscopy of hydrogen is often limited by the second-order Doppler effect. To determine this effect, we apply a magnetic field perpendicular to the atomic beam. This field induces a quadratic motional Stark shift proportional, as the second-order Doppler effect, to v(2) (v atomic velocity). For some magnetic field, these two effects are opposite and the total shift due to the atomic velocity is reduced. We present the first observation of this effect for the 1S-3S transition in hydrogen.
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 report observation of the 1S-2S two-photon transition in hydrogen confined in a magnetic trap at submillikelvin temperatures. The excitation spectrum can display a sharp central feature arising from periodic motion of the trapped atoms. The metastable 2S atoms remain trapped, and have a lifetime close to the natural lifetime of 122 ms. These developments open the way to achieving the transition's natural linewidth. We have also demonstrated that the temperature of the gas can be determined from the line shape, providing an important tool for the study of cold trapped hydrogen. The resolution in these experiments appears to be limited by laser stability, currently 3 kHz.