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Physical Review A

Doppler-free Stark spectroscopy of the second excited level of atomic hydrogen for measurements of electric fields

M. Gemisic Adamov, Andreas Steiger, Klaus Grutzmacher, Joachim Seidel

Published Jan 11, 2007• 15 citations
Publisher

Abstract

The Stark splitting of the second excited level of atomic hydrogen (with principal quantum number $n=3$) 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 $205\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ allows us to measure the $n=3$ 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 $200\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm}$. 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 $50\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm}$ 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.

DOI
10.1103/physreva.75.013409

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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-\ensuremathα\ensuremath{\alpha}\ensuremathα 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.
Fluorescence-dip spectroscopy based on an optical double resonance is used to probe the Stark splitting in highly excited Rydberg states of atomic hydrogen. After Doppler-free two-photon excitation to n=3n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3n=3, fluorescence at Balmer $\ensuremath{\alpha}$ is observed. When the radiation of a second laser is tuned over the resonance between n=3n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3n=3 and a Rydberg state, the Stark splitting manifests itself as a series of dips in the Balmer- $\ensuremath{\alpha}$ fluorescence intensity. Rydberg states up to n=55n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}55n=55 can be identified. The minimum detectable electric field is 5V/cm5\mathrm{V}/\mathrm{cm}5V/cm. This is about an order of magnitude more sensitive than other laser-induced fluorescence techniques.
The Stark spectroscopy of the hydrogen atom has been investigated near the ionization threshold in static homogeneous external electric fields from \ensuremath{\sim}1000 to \ensuremath{\sim}8000 V/cm with use of a two-step excitation H(n=1)+\ensuremath{\Elzxh}${\ensuremath{\omega}}_{\mathrm{vuv}\ensuremath{\rightarrow}}$H(n=2)+\ensuremath{\Elzxh}\ensuremath{\omega} $_{\mathrm{uv}\ensuremath{\rightarrow}}$H∗{\mathrm{H}}^{\mathrm{*}}H∗ with vuv and uv laser radiation, independently tunable and linearly polarized either parallel (\ensuremath{\pi}) or perpendicular (\ensuremath{\sigma}) with respect to the external field. Different from other, nonhydrogenic atoms, the hydrogen atom is a peculiar case insofar as the initial states of H(n=2), from which excitation takes place, are essentially of parabolic character at the field strengths employed in this study.Individual sublevels (n1{n}_{1}n1​,n2{n}_{2}n2​,\ensuremath{\Vert}ml{m}_{l}ml​\ensuremath{\Vert}) have been prepared in the n=2 state with sub-Doppler resolution. Photoionization spectra have been obtained with \ensuremath{\pi}- and \ensuremath{\sigma}-polarized uv radiation from the four possible sublevels of the n=2 Stark manifold: \ensuremath{\Vert}1,0,0〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉, \ensuremath{\Vert}0,1,0〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉, \ensuremath{\Vert}0,0,\ifmmode\pm\else\textpm\fi{}1〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉, and \ensuremath{\Vert}0,0,\ensuremath{\mp}1〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉. All spectra show sharp line structures of quasistable field-ionizing states superimposed on continua in the energy region between the classical saddle point, ${E}_{\mathrm{SP}=\mathrm{\ensuremath{-}}2\phantom{\rule{0ex}{0ex}}\mathrm{\ensuremath{\surd}}\mathrm{F}}$ a.u., and the zero-field ionization threshold E=0 a.u. Employing existing theoretical treatments, the quasistable spectral structures are quantitatively completely analyzed and accounted for, as long as their field ionization rate is less than \ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}1011{10}^{11}1011 ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$. Field-ionization rates of quasistable states have been measured and are compared with theory. Oscillatory resonance structures of the ionization cross section near the zero-field threshold are observed with pronounced modulation degree only in the spectrum from the \ensuremath{\Vert}1,0,0〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉 sublevel excited with the uv \ensuremath{\pi}-polarized. The energy spacing of the oscillations has been measured as a function of the electric field strength F and found to be nearly proportional to F3/4{F}^{3/4}F3/4, with slight but definite deviations. Theoretical analysis of the oscillations yields quantitative agreement with the experiment.
Two synchronised pulsed single-mode tunable laser systems are used to excite atomic hydrogen in an atomic beam. A vacuum ultraviolet (VUV) laser populates first the 2p 2 P 3/2 sublevel from the ground 1s 2 S 1/2 state. A second-step UV laser selects substates of the n=33 manifold in the presence of a weak electric field (23.6 V cm -1 ). Stark patterns of this manifold are recorded for different polarisation configurations of the exciting light beams. The n=44 substates are detected by the standard field ionisation technique. The measured relative intensities of the Stark components agree with the theoretical excitation probabilities in the two-step process, calculated to the first order of perturbation theory.
The prediction of the energy level shifts and intensity transfer in atomic hydrogen and helium spectra caused by an external electric field was one of the first applications of wave mechanics. Early measurements relied on electrical discharge sources for excited atoms; since discharge processes will not produce excited states with n > 7 in observable densities, very large (10s to 100s kV cm) electric fields were required to resolve spectral modifications. The development of high peak power lasers enabled excitation to high n (Rydberg) states, increasing field sensitivity down to millivolts/cm and allowing comparison of experiment and theory in well-defined conditions. Field modified selection rules can be used to measure the field direction as well as magnitude. Analysis of line shape simulations of Stark modified Rydberg spectra reveals pitfalls in commonly used field measurement techniques. An ambiguity in defining series termination results in a factor of 2 discrepancy in field measurements based on Inglis Teller line merging. Field-induced line broadening (unresolved manifold splitting) in triplet and singlet helium are shown to differ significantly, with triplet broadening nonlinear with field.
Rydberg states of atomic helium with principal quantum numbers ranging from n=20n=20n=20 to n=100n=100n=100 have been prepared by non-resonance-enhanced single-color two-photon excitation from the metastable 23S12\phantom{\rule{0.16em}{0ex}}{{}^{3}S}_{1}23S1​ state. Photoexcitation was carried out using linearly and circularly polarized pulsed laser radiation. In the case of excitation with circularly polarized radiation, Rydberg states with azimuthal quantum number $|{m}_{\ensuremath{\ell}}|=2$ were prepared in zero electric field and in homogeneous electric fields oriented parallel to the propagation axis of the laser radiation. In sufficiently strong electric fields, individual Rydberg--Stark states were resolved spectroscopically, highlighting the suitability of non-resonance-enhanced multiphoton excitation schemes for the preparation of long-lived high-$|{m}_{\ensuremath{\ell}}|$ hydrogenic Rydberg states for deceleration and trapping experiments. Applications of similar schemes for Doppler-free excitation of positronium atoms to Rydberg states are also discussed.
Abstract We produce Rydberg Ps by a two-step laser excitation from and from to states of principal quantum level that are Stark split by a motionally induced electric field. Our measurements are largely free of first-order Doppler shifts such that we are able to investigate the impact of laser polarization on the population of the closely spaced Stark levels. We find a variation in the distribution that is primarily dependent on the IR laser polarization with respect to the direction of the motionally induced electric field. With the IR light polarized parallel to the electric field F , the ratio of excitation probability to the levels of maximal Stark splitting compared to that of excitation to the states of minimal Stark splitting is found to be 3.37 ± 0.51, whereas with the IR light polarized perpendicular to F , the excitation ratio is 0.87 ± 0.64. Our results agree with those of Wall et al (2015 Phys. Rev. Lett. 114 173001 ) obtained with n = 11 and will be useful in the preparation of high- n states of Ps for a variety of experiments, including measuring the interaction of Ps with gravity, in precision time-of-flight (TOF) energy spectroscopy, and precision optical spectroscopy of Ps.