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Physical Review Letters

Observation of Electric-Field-Induced Resonances above the Ionization Limit in a One-Electron Atom

Richard R. Freeman, Nicholas P. Economou, Gary C. Bjorklund, K. T. Lu

Published Nov 20, 1978• 119 citations
Publisher

Abstract

Measurements of the relative photoionization cross sections of Rb in the presence of various strengths of external electric fields are reported. Systematic, field-dependent, resonance structure is observed not only for energies above the classical field-ionization limit, but above the zero-field ionization limit as well. A striking dependence of the cross section upon light polarization is also observed.

DOI
10.1103/physrevlett.41.1463

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Measurements of the relative photoionization cross sections of Rb in the presence of various strengths of external electric fields are reported. Systematic, field-dependent, resonance structure is observed not only for energies above the classical field-ionization limit, but above the zero-field ionization limit as well. A striking dependence of the cross section upon light polarization is also observed.
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.
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.
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.
We have observed large oscillations in the photoabsorption cross sections of Ba and Na in the presence of an electric field. The two-step laser excitation technique allowed the use of various polarization combinations for studying the oscillations in the vicinity of the zero-field ionization limits. Thus, we could for the first time determine the relative contributions from two entirely different theoretical models: The quasibound m=0m=0m=0 states (strong-field-mixing resonances) on the one hand, and symmetry-induced oscillator-strength cancellations on the other. We found that the model of strong-field-mixing resonances alone is able to account for all our experimentally observed cross-section oscillations.
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.
Experimental results on the photoionization spectra of excited rubidium atoms in a well-defined ml=1{m}_{l}=1ml​=1 state in the presence of an electric field are reported. Spectra corresponding to a definite polarization of the ionizing light exhibit characteristic resonances which are ascribed either to the non-Coulombic part of the central potential or to the spin-orbit interaction. The different line profiles are interpreted as being due to interferences between discrete states and continua, the observed structures depending directly on the density of oscillator strengths and not simply on the density of continuum states.