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Physical Review A

Electric field dependence of the photoionization cross section of Rb

Richard R. Freeman, Nicholas P. Economou

Published Dec 1, 1979• 92 citations
Publisher

Abstract

The relative photoionization cross section of ground-state Rb is measured near threshold as a function of applied electric field strength. The cross section is found to have a wavelength-dependent resonance structure that changes with the strength of the electric field. This resonance structure is observed not only for energies above the classical field ionization limit, but for the case of $\ensuremath{\pi}$ excitation, beyond the zero-field ionization limit as well. An analysis of the data is presented that connects the concepts of "strong-field mixing" and the perturbation calculations of the energies of hydrogenic Stark components.

DOI
10.1103/physreva.20.2356

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The relative photoionization cross section of ground-state Rb is measured near threshold as a function of applied electric field strength. The cross section is found to have a wavelength-dependent resonance structure that changes with the strength of the electric field. This resonance structure is observed not only for energies above the classical field ionization limit, but for the case of \ensuremathπ\ensuremath{\pi}\ensuremathπ excitation, beyond the zero-field ionization limit as well. An analysis of the data is presented that connects the concepts of "strong-field mixing" and the perturbation calculations of the energies of hydrogenic Stark components.
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.
Exact calculations of the photoionization cross sections of ground-state H in the presence of an external electric field are presented. The oscillations obtained above the zero-field ionization limit for $\ensuremath{\pi}$ polarization do not arise from specific properties of m=0m=0m=0 states, but from cancellation effects in the oscillator strengths due to the symmetry properties of the wave functions and of the light. The dependence of the cross section upon the light polarization is thoroughly explained and agrees with recent experiments on Rb.
Stark spectra of barium Rydberg states above the classical field-ionization limit have been recorded at high density of states employing high-resolution laser spectroscopy. The spectra, taken at a binding energy of about \ensuremath{\varepsilon}\ensuremath{\approxeq}-55 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with respect to zero-field threshold and at electric-field strengths F\ensuremath{\approxeq}100 V/cm exhibit dramatic variations in line profiles with increasing external field strength. The WKB quantum-defect theory of the Stark effect of nonhydrogenic atoms was used to analyze the recorded spectra, and excellent agreement between measured and calculated line profiles was achieved. Core-induced coupling of closed and open hydrogenic Stark channels was found to contribute dominantly to the linewidth of the recorded Stark resonances. In addition, a reformulation of this theory by McNicholl, Ivri, and Bergeman (unpublished) in terms of a configuration-interaction model was employed to analyze a particular avoided crossing of several Stark components. In this way recorded line profiles were parametrized within a limited model to obtain resonance energies, linewidths, and Fano q parameters.
Laser investigation of the photoionization spectra in the presence of an electric field has been performed in $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ polarizations on an ytterbium atomic beam from the particular level 4f146s7s1S04{f}^{14}6s7s^{1}S_{0}4f146s7s1S0​ which was populated by a two-step excitation. Broad modulations (in $\ensuremath{\pi}$ polarization) and Stark resonances in the vicinity of the zero-field ionization limit are interpreted satisfactorily as in the case of alkali atoms. However, the photoionization spectra are deeply affected by the presence of two perturbing levels belonging to the configuration 4f135d26s4{f}^{13}5{d}^{2}6s4f135d26s. This phenomenon is explained by strong interference effects between the structured Stark continuum and the field-induced autoionizing states corresponding to the doubly excited levels.
This paper summarizes a long series of experiments that have been done on Rydberg states of Rb. The basic experimental technique that has been used is atomic-beam laser spectroscopy which allows both low-resolution and high-resolution studies. Excitation of Rydberg states is provided by single-photon absorption from a suitably frequency-doubled rhodamine 6G6G6G tunable laser. Detection is done by field ionization and ion counting. These techniques have allowed us to study the critical ionizing field, which has been found to follow classical, hydrogenic behavior closely. Rydberg states of Rb have been observed from n=28n=28n=28 up to n>100n>100n>100. High-resolution spectroscopic studies have led to measurement of the fine structure for np\mathrm{np}np levels located between n=28n=28n=28 and n=60n=60n=60, as well as the isotope shift of the ground state, $\ensuremath{\delta}\ensuremath{\nu}=(172\ifmmode\pm\else\textpm\fi{}15)$ MHz. Anomalies in the intensity ratio of the doublet $5s\ensuremath{-}np$ transitions have been observed and interpreted as relativistic effects. Perturbations by weak and strong dc electric field are reported. In the case of weak electric fields it is possible to evaluate the polarizability. In the case of strong dc electric fields, new phenomena have been observed and analyzed. We also find experimental evidence of selective photoionization in the presence of an appropriate dc electric field, which could have some applications in laser isotope separation. Finally, we give the preliminary results of an experiment on the effect of a strong nonresonant electromagnetic field on high-lying Rydberg states.