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Physical Review A

Stark beats of Ar Rydberg states

Yumio Morioka, Tomohiro Aoto, H. Yoshii

Published Oct 15, 2001• 7 citations
Publisher

Abstract

Vacuum ultraviolet fluorescence decay spectra of Ar atom resonance lines excited by pulsed vacuum ultraviolet light in a synchrotron single bunch operation were obtained under a static electric field. When an atom under the static electric field was excited simultaneously to both the magnetic sublevels $M=0$ and $|M|=1$ by polarized light and the observation area was asymmetric, Stark beats were observed in the fluorescent decay spectra. All observed beat frequencies varied proportionally to the square of the external electric field. The results for $8d$ and $9d$ doublet lines were compared with those obtained by the usual second order perturbation theory, assuming mixing ratios between three $\mathrm{jl}$ coupling scheme d-type states. The beat frequencies were also measured for other resonance lines.

DOI
10.1103/physreva.64.053409

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Vacuum ultraviolet fluorescence decay spectra of Ar atom resonance lines excited by pulsed vacuum ultraviolet light in a synchrotron single bunch operation were obtained under a static electric field. When an atom under the static electric field was excited simultaneously to both the magnetic sublevels M=0M=0M=0 and ∣M∣=1|M|=1∣M∣=1 by polarized light and the observation area was asymmetric, Stark beats were observed in the fluorescent decay spectra. All observed beat frequencies varied proportionally to the square of the external electric field. The results for 8d8d8d and 9d9d9d doublet lines were compared with those obtained by the usual second order perturbation theory, assuming mixing ratios between three jl\mathrm{jl}jl coupling scheme d-type states. The beat frequencies were also measured for other resonance lines.
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-$\ensuremath{\alpha}$ 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 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 observation of the Stark-tuned Förster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the Förster resonance. In our experiments with a few cold Rb Rydberg atoms we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the Förster resonances, since the population transfer at the resonances occurs on a time scale of $\sim$100 ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted Förster resonances, while non-sharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the Förster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned Förster resonances Rb(nP3/2)+Rb(nP3/2)→Rb(nS1/2)+Rb([n+1]S1/2){\rm Rb}(nP_{3/2} )+{\rm Rb}(nP_{3/2} )\to {\rm Rb}(nS_{1/2} )+{\rm Rb}([n+1]S_{1/2} )Rb(nP3/2​)+Rb(nP3/2​)→Rb(nS1/2​)+Rb([n+1]S1/2​) for two Rb Rydberg atoms interacting in a time-varying electric field.
The observation of the Stark-tuned F\"orster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the F\"orster resonance. In our experiments with a few cold Rb Rydberg atoms, we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the F\"orster resonances, since the population transfer at the resonances occurs on a time scale of $\ensuremath{\sim}100$ ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted F\"orster resonances, while nonsharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the F\"orster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned F\"orster resonances $\mathrm{Rb}(n{P}_{3/2})+\mathrm{Rb}(n{P}_{3/2})\ensuremath{\rightarrow}\mathrm{Rb}(n{S}_{1/2})+\mathrm{Rb}([n+1]{S}_{1/2})$ for two Rb Rydberg atoms interacting in a time-varying electric field.
Quantum computing and quantum simulation with ultracold neutral atoms require Rydberg excitation of individual atoms in atomic arrays. Rydberg states are extremely sensitive to external electric fields, therefore precise three-dimensional control of the electric field is essential. We performed a spectroscopic study of three-photon Rydberg excitation of a single Rb atom in an optical dipole trap in the presence of an external DC electric field. The field was generated by eight electrodes deposited on the inner surfaces of an ultrahigh-vacuum glass cell. The used three-photon scheme of laser excitation of Rydberg \textit{nP} states allows the Stark shift and the splitting of the resonances to be observed simultaneously, which simplifies calibration of the electric field. In addition, in the commonly used two-photon Rydberg excitation schemes, the light shifts can complicate accurate determination of the DC Stark shift, particularly when the external electric field is scanned across different spatial directions, and different Stark components are excited. These shifts are absent in the three-photon excitation scheme used in our experiment. We demonstrated the ability to independently tune the electric field along all three spatial directions and to compensate for stray electric fields. The measured three-photon spectra exhibit Stark shifts and splittings of the three-photon resonance that are in good agreement with theoretical calculations. These results are also of interest for Rydberg electrometry.
Intensity beats in the emission of $\mathrm{L}{\mathrm{y}}_{\ensuremath{\alpha}}$ from beam-foil excited hydrogen in various static electromagnetic field configurations have been studied. The observed beat frequencies agree with the calculated values, which are independent of the field directions. The beat amplitudes, however, show significant dependence on the field directions relative to the beam. The theory for emission of light from the decay of coherently excited states is applied in the sudden perturbation limit. Agreement with experiment can only be obtained under the assumption that the foil excitation generates initial coherent wave functions ${\ensuremath{\Psi}}_{\mathrm{I},\mathrm{I}\mathrm{I}}=\ensuremath{\alpha}|p,\frac{1}{2},\ifmmode\pm\else\textpm\fi{}\frac{1}{2}〉+\ensuremath{\beta}|s,\frac{1}{2},\ensuremath{\mp}\frac{1}{2}〉$, where ∣l,j,mj〉|l,j,{m}_{j}〉∣l,j,mj​〉 notation and the beam as quantization axis are used. The ratio $\frac{\ensuremath{\alpha}}{\ensuremath{\beta}}$ is then determined, which gives the ratio of the excitation cross section of the ppp to that of the sss states as $\frac{{\ensuremath{\sigma}}_{p}}{{\ensuremath{\sigma}}_{s}}>~4\ifmmode\pm\else\textpm\fi{}1$ at a beam energy of 200 (keV) per atom.