Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Photoabsorption of Ba and Na in an electric field: Manifestation of strong-field-mixing resonances

Wolfgang Sandner, Kambiz Ali Safinya, Thomas F. Gallagher

Published May 1, 1981• 40 citations
Publisher

Abstract

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 $m=0$ 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.

DOI
10.1103/physreva.23.2448

Related papers

Interpretation of Electric-Field-Induced Oscillations in the Cross Section of a One-Electron Atom above the Ionization Limit

Eliane Luc-Koenig, Annik Bachelier

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 $m=0$ 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.

Physical Review Letters•Sep 24, 1979•57 citations

Electric field dependence of the photoionization cross section of Rb

Richard R. Freeman, Nicholas P. Economou

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.

Physical Review A•Dec 1, 1979•92 citations

CONTINUUM STARK SPECTROSCOPY

Louis F. DiMauro, T. H. Bergeman, Patrick J. McNicholl +1 more

We have studied experimentally and theoretically two-step photoionization through the 3P state of sodium in an electric field of up to 3.90 kV/cm. The apparatus uses an atomic beam crossed by two pulsed laser beams, one at 589 nm for the first step, and the other swept through the zero field threshold Eo near 409 nm for the ionization. We observe broad undulations in the photocurrent above Eo that narrow with decreasing energy and eventually sharpen into well-defined but asymmetric transitions to Stark-shifted Rydberg states. We calculate the oscillator strength density for the appropriate transitions using modified hydrogenic wave functions and find excellent agreement for the position and relative strength of all the spectral features. We model the asymmetries as Fano-type interferences between quasi-discrete and continuum ionization channels. Using appropriate core potentials, and taking into account core-induced coupling of both discrete-to-continuum and continuum-to-continuum states, we obtain estimates of Fano's q and Ɖ that agree reasonably well with our measurements.

Le Journal de Physique Colloques•Nov 1, 1982•3 citations

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

Richard R. Freeman, Nicholas P. Economou, Gary C. Bjorklund +1 more

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.

Physical Review Letters•Nov 20, 1978•119 citations

Experimental studies of three-photon ionization of Ba: Evidence of channel interference and Raman coupling

James Floyd Kelly, Jan P. Hessler, G. Alber

Three-photon ionization spectra of Ba were studied which result from two-photon resonances between the 6${s}^{2}$ ${\mathrm{}}^{1}$${S}_{0}$ ground state and the 6snd J=2,6s(n+1)s ${\mathrm{}}^{1}$${S}_{0}$ (16\ensuremath{\le}n40) Rydberg states and 5d7d ${\mathrm{}}^{1}$${D}_{2}$,${\mathrm{}}^{3}$${P}_{0}$,2 perturber states. A tunable laser with field strength ${10}^{\mathrm{\ensuremath{-}}(4\mathrm{\ensuremath{-}}5)}$ a.u. was used to drive the excitation in a low-density atomic beam (n\ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$). Resonant line shapes were systematically studied as a function of light polarization and intensity. Studies with linearly polarized light find all resonant line shapes manifest the same peak shift and asymmetry which is traced to the ac Stark shift of the ground state. The resonant peak height, shift, and linewidth scale linearly with light intensity which is accounted for with a rate-equation formulation.For the case of circular polarization, a distinct minimum of ionization occurs between each J=2 doublet of the 6snd series. One level (generally $^{3}\mathrm{D}_{2}$) is significantly broadened in comparison to the laser linewidth (0.1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) with increasing intensity while its sister level remains narrow (\ensuremath{\sim}0.2 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Further, light shifts of the $^{3}\mathrm{D}_{2}$ states are generally \ensuremath{\gtrsim}1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ to the red while shifts of $^{1}\mathrm{D}_{2}$ states are negligible. This behavior switches for the n=27 doublet. Lastly, the dynamic shifts are not quadratic with the field strength. These effects are attributed in part to cancellation due to channel interference and a two-photon Raman process which mixes each J=2 doublet. These processes act in conjunction with the ac Stark effect to produce the observed profile behavior. The shifts and coupling of the excited states are attributed to the influence of the 6pnd ${J}^{\ensuremath{\pi}}$${=3}^{\mathrm{\ensuremath{-}}}$ autoionization series and are shown to be sensitive to the singlet-triplet mixing coefficient \ensuremath{\beta} of the J=2 doublets. A perturbation analysis is introduced which accounts for the salient features of the data, although it does not include bandwidth and saturation effects. Calculations of light shifts of the 6snd J=2 levels based on this analysis require \ensuremath{\beta} be modified from previous assignments based on hfs measurements for n in the vicinity of the 5d7d ${\mathrm{}}^{1}$${D}_{2}$ perturber.

Physical Review A•Jun 1, 1986•10 citations

Resonance spectra of Ba Rydberg atom in electric field above the ionization limit

Jiakun Xu, Wenjie Yu, Qing Ye

Stark spectra of barium Rydberg states above the classical field-ionization limit have been recorded employing high-resolution laser spectroscopy with π and σ polarization.The resonance structure is observed obviously in experiment, and the theoretical calculations considering the core effect are well in coincidence with the experimental observation.

International Photonics and Optoelectronics Meetings•Jan 1, 2017•0 citations
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.
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 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.
We have studied experimentally and theoretically two-step photoionization through the 3P state of sodium in an electric field of up to 3.90 kV/cm. The apparatus uses an atomic beam crossed by two pulsed laser beams, one at 589 nm for the first step, and the other swept through the zero field threshold Eo near 409 nm for the ionization. We observe broad undulations in the photocurrent above Eo that narrow with decreasing energy and eventually sharpen into well-defined but asymmetric transitions to Stark-shifted Rydberg states. We calculate the oscillator strength density for the appropriate transitions using modified hydrogenic wave functions and find excellent agreement for the position and relative strength of all the spectral features. We model the asymmetries as Fano-type interferences between quasi-discrete and continuum ionization channels. Using appropriate core potentials, and taking into account core-induced coupling of both discrete-to-continuum and continuum-to-continuum states, we obtain estimates of Fano's q and Ɖ that agree reasonably well with our measurements.
Three-photon ionization spectra of Ba were studied which result from two-photon resonances between the 6s2{s}^{2}s2 1{\mathrm{}}^{1}1S0{S}_{0}S0​ ground state and the 6snd J=2,6s(n+1)s 1{\mathrm{}}^{1}1S0{S}_{0}S0​ (16\ensuremath{\le}n40) Rydberg states and 5d7d 1{\mathrm{}}^{1}1D2{D}_{2}D2​,3{\mathrm{}}^{3}3P0{P}_{0}P0​,2 perturber states. A tunable laser with field strength ${10}^{\mathrm{\ensuremath{-}}(4\mathrm{\ensuremath{-}}5)}$ a.u. was used to drive the excitation in a low-density atomic beam (n\ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}108{10}^{8}108 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$). Resonant line shapes were systematically studied as a function of light polarization and intensity. Studies with linearly polarized light find all resonant line shapes manifest the same peak shift and asymmetry which is traced to the ac Stark shift of the ground state. The resonant peak height, shift, and linewidth scale linearly with light intensity which is accounted for with a rate-equation formulation.For the case of circular polarization, a distinct minimum of ionization occurs between each J=2 doublet of the 6snd series. One level (generally 3D2^{3}\mathrm{D}_{2}3D2​) is significantly broadened in comparison to the laser linewidth (0.1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) with increasing intensity while its sister level remains narrow (\ensuremath{\sim}0.2 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Further, light shifts of the 3D2^{3}\mathrm{D}_{2}3D2​ states are generally \ensuremath{\gtrsim}1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ to the red while shifts of 1D2^{1}\mathrm{D}_{2}1D2​ states are negligible. This behavior switches for the n=27 doublet. Lastly, the dynamic shifts are not quadratic with the field strength. These effects are attributed in part to cancellation due to channel interference and a two-photon Raman process which mixes each J=2 doublet. These processes act in conjunction with the ac Stark effect to produce the observed profile behavior. The shifts and coupling of the excited states are attributed to the influence of the 6pnd ${J}^{\ensuremath{\pi}}$${=3}^{\mathrm{\ensuremath{-}}}$ autoionization series and are shown to be sensitive to the singlet-triplet mixing coefficient \ensuremath{\beta} of the J=2 doublets. A perturbation analysis is introduced which accounts for the salient features of the data, although it does not include bandwidth and saturation effects. Calculations of light shifts of the 6snd J=2 levels based on this analysis require \ensuremath{\beta} be modified from previous assignments based on hfs measurements for n in the vicinity of the 5d7d 1{\mathrm{}}^{1}1D2{D}_{2}D2​ perturber.