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Physical Review Letters

Observation of a Motional Stark Effect to Determine the Second-Order Doppler Effect

G. Hagel, Rémy Battesti, F. Nez, Lucile Julien, F. Biraben

Published Oct 23, 2002• 22 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.89.203001

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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.
We have observed transitions between Rydberg states of He with sub-Doppler resolution, using a novel technique. Ordinary Doppler line shapes, observed at low magnetic fields, are completely altered at high fields by the quadratic Stark effect induced by velocity-dependent electric fields arising from atomic motion transverse to the magnetic field. The high-field line shape has an abrupt cutoff, corresponding to ${v}_{\ensuremath{\perp}}\ensuremath{\simeq}0$ atoms, whose slope is primarily limited by the homogeneous linewidth.
The Stark splitting of the second excited level of atomic hydrogen (with principal quantum number n=3n=3n=3) has been measured by pulsed laser spectroscopy in order to determine small electric fields by optical means. Doppler-free excitation with two counterpropagating laser beams at 205nm205\phantom{\rule{0.3em}{0ex}}\mathrm{nm}205nm allows us to measure the n=3n=3n=3 Stark spectra either by an optogalvanic signal after ionization by a third laser photon or by detection of the Balmer-$\ensuremath{\alpha}$ fluorescence photons emitted by the excited atoms. Three different cases of laser polarization have been investigated in order to evaluate the possibilities and limitations of this one-step laser excitation method for electric field determination, especially at field strengths below 200V∕cm200\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm}200V∕cm. The method provides the best field sensitivity achieved with lower excited levels that can be reached directly by two-photon absorption from the ground state (in contrast to the more sensitive Rydberg levels). For this purpose, an advanced tunable pulsed uv laser with narrow bandwidth almost at the Fourier limit has been used. The high spectral resolution allowed us to deduce electric field strengths as small as 50V∕cm50\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm}50V∕cm from the frequency shift between two selected isolated Stark components. As a main advantage, this simple analysis of the measured spectra does not rely on knowledge of the line intensities which may be strongly affected by the measuring conditions.
Atoms moving through a magnetic field suffer a Stark effect whose magnitude is dependent upon the atom's velocity. This velocity-dependent perturbation has recently been exploited as a Doppler narrowing technique, and in this paper we consider atomic anticrossings induced by it. Experimentally such anticrossings are observed between $n^{3}D\ensuremath{-}n^{1,3}F$ states of He for $n=4\ensuremath{-}9$, with n=8n=8n=8 being considered in detail. Theoretical expressions are derived for motional-Stark-effect-induced anticrossing line shapes. Good agreement with the observed line shapes is obtained and the theoretical analysis allows a value of the $n=^{3}D\ensuremath{-}^{1,3}F$ interval to be obtained which is in good agreement with previous predictions.
We have observed the second-order, field-induced Zeeman effects of the Doppler-free two-photon transitions 52{\mathrm{}}^{2}2S--32{\mathrm{}}^{2}2S and 42{\mathrm{}}^{2}2D--32{\mathrm{}}^{2}2S of atomic sodium using fields up to 5 T. Using a suitable experimental configuration it was possible to avoid the appearance of first-order effects in the high-field limit. The remaining small field-induced shifts are of the order of magnitude of a few linewidths. They yield the differences of the diamagnetic susceptibilities of the connected atomic states. The method is therefore capable of providing data related to atomic electronic structure. \textcopyright{} 1996 The American Physical Society.