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Physical Review Letters

Linear Stark Effect Due to Resonant Interactions of Static and Dynamic Fields

Arthur Cohn, Pradip M. Bakshi, Gabor J. Kalman

Published Aug 7, 1972• 38 citations
Publisher

Abstract

We investigated the line shape of the Lyman-$\ensuremath{\alpha}$ transition of a hydrogen atom simultaneously subjected to a static and a perpendicular high-frequency electric field. It was found that resonance effects occur, producing a profile substantially different from the Stark spectrum of the fields acting independently. This result shows that the interpretation of turbulent hydrogen plasma spectra by the Blokhintsev (dynamic field only) theory is not generally valid.

DOI
10.1103/physrevlett.29.324

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The nonlinear low-field Stark effect in the level n=2 of hydrogen has been investigated. \nThe experiment employed the level crossing technique, measuring the position of the crossings between the Zeeman states: \n2P3/2, mj=-3/2 and 2P1/2, mj=1/2; and \n2P3/2, mj=-3/2 and 2S1/2, mj=1/2; \nas the electric field was varied from 0 to 500 kV/m. \nA beam of atomic hydrogen, produced by thermal dissociation, was subjected to parallel electric and magnetic fields. Lymman –α (Lyα) resonance radiation was generated in an electrodeless microwave discharge lamp. The profile of the Lyα line emitted by the lamp has been investigated experimentally. \nThe level crossings were detected as changes of the Lyα resonance fluorescence intensity observed in a certain direction. The crossing positions were determined from the observed crossing signals of Lorentzian profile by a least squares computer programme. \nThe experimental results for the crossing positions as afuction of the electric field have been compared with theoretical calculations. The theoretical values were obtained by numerical diagonalization of the matrix of the eigenstates |2ℓjFmF> for perturbation by combined electric and magnetic fields. Radiative corrections were included. \nTheoretical values and experimental results agreo within the experimental uncertainties of 2%.

•Jan 1, 1974•0 citations
We investigated the line shape of the Lyman-\ensuremathα\ensuremath{\alpha}\ensuremathα transition of a hydrogen atom simultaneously subjected to a static and a perpendicular high-frequency electric field. It was found that resonance effects occur, producing a profile substantially different from the Stark spectrum of the fields acting independently. This result shows that the interpretation of turbulent hydrogen plasma spectra by the Blokhintsev (dynamic field only) theory is not generally valid.
Atomic absorption spectra of the He I plasma in the static magnetic field in the absence of laser radiation are different from spectra in the presence of laser radiation. Especially, it has been theoretically predicted that the spectral shift of the satellite line, which is seen in the latter case, does not exist in the former case. In this paper, the effect of three-dimensional high-frequency electric fields on the σ+, σ−, and π components of the allowed 1 1S0-3 1P1 transition and the forbidden 1 1S0-3 1D2 lines in atomic absorption spectra of the He I plasma in a static magnetic field in the absence of a laser beam is investigated from the coupled equations for the probability amplitudes of atomic states. It is shown that they should give rise to a spectral shift of the allowed lines and satellites about forbidden lines. The calculation reveals that the shift is proportional to the mean-square stochastic electric field, and that the ratio of the intensity of the near satellite to that of the far satellite is different from the ratio obtained by the second-order perturbation theory or the three-level rotating-wave approximation. Discussion is given for the validity of this theory.
The intensity distribution in the core region of the Lyman-$\ensuremath{\alpha}$ line of hydrogen perturbed by neutral hydrogen atoms in the presence of an external cone-rotating electric field has been evaluated using an impact approximation. It was found that the line shape in this region can be described as the sum of four Lorentzian profiles representing contributions coming from transitions between various Stark and Berry sublevels of the resonance and ground states of the hydrogen atom. The effects due to Berry's phase are shown to produce a Lorentzian-shaped feature on each side of the Lyman-$\ensuremath{\alpha}$ line, with maxima located at frequencies linearly dependent on the angular frequency with which the electric field rotates about the laboratory fixed zzz axis, as well as on the cosine of the polar angle that the field makes with respect to this axis. The remaining two Lorentzian profiles are due to the Stark effect, and their maxima are located on both sides of the Lyman-$\ensuremath{\alpha}$ line at frequencies corresponding to the Stark shift.
We report on an experimental and theoretical study of the dynamic (ac) Stark effect on a forbidden transition. A general framework for parametrizing and describing off-resonant ac-Stark shifts is presented. A model is developed to calculate spectral line shapes resulting from resonant excitation of atoms in an intense standing light wave in the presence of off-resonant ac-Stark shifts. The model is used in the analysis and interpretation of a measurement of the ac-Stark shifts of the static-electric-field-induced $6{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5d6s^{3}D_{1}$ transition at 408nm408\phantom{\rule{0.3em}{0ex}}\mathrm{nm}408nm in atomic Yb. The results are in agreement with estimates of the ac-Stark shift of the transition under the assumption that the shift is dominated by that of the 6s21S06{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}6s21S0​ ground state. A detailed description of the experiment and analysis is presented. A biproduct of this work is an independent determination (from the saturation behavior of the 408-nm transition) of the Stark transition polarizability, which is found to be in agreement with our earlier measurement. This work is part of the ongoing effort aimed at a precision measurement of atomic parity-violation effects in Yb.
General equations are presented for determining the field-dependent variation of the wavefunctions, matrix elements and intensities of dipole transitions between Stark levels of a hydrogen atom in a field range where the fine-structure effects may be neglected. The Sturm-series resolution for the reduced Coulomb-Green function is used to derive analytical expressions for the first-order corrections in terms of parabolic quantum numbers of initial and final states. Simple forms of these expressions as functions of the upper-state quantum numbers are presented explicitly for the Lyman and Balmer series. The selective action of the dc electric field on the intensity of Stark components of hydrogen lines is revealed in numerical calculations for both and types of emitted radiation. This selectivity may cause, in particular, enhancement of the high-frequency and damping of the low-frequency Stark -lines of the Lyman series.
The nonlinear low-field Stark effect in the level n=2 of hydrogen has been investigated. \nThe experiment employed the level crossing technique, measuring the position of the crossings between the Zeeman states: \n2P3/2, mj=-3/2 and 2P1/2, mj=1/2; and \n2P3/2, mj=-3/2 and 2S1/2, mj=1/2; \nas the electric field was varied from 0 to 500 kV/m. \nA beam of atomic hydrogen, produced by thermal dissociation, was subjected to parallel electric and magnetic fields. Lymman –α (Lyα) resonance radiation was generated in an electrodeless microwave discharge lamp. The profile of the Lyα line emitted by the lamp has been investigated experimentally. \nThe level crossings were detected as changes of the Lyα resonance fluorescence intensity observed in a certain direction. The crossing positions were determined from the observed crossing signals of Lorentzian profile by a least squares computer programme. \nThe experimental results for the crossing positions as afuction of the electric field have been compared with theoretical calculations. The theoretical values were obtained by numerical diagonalization of the matrix of the eigenstates |2ℓjFmF> for perturbation by combined electric and magnetic fields. Radiative corrections were included. \nTheoretical values and experimental results agreo within the experimental uncertainties of 2%.