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Physical Review A

Precision measurement of the 5st2 S1/2 → 5pt2 Pj → 8st2 S1/2 two-photon, two-color polarization spectrum in atomic Rb

A. I. Beger, Mark D. Havey, Rodney P. Meyer

Published May 1, 1997• 9 citations
Publisher

Abstract

Precision measurements on the 5s${\mathrm{}}^{2}$${\mathrm{S}}_{1\mathrm{/}2}$\ensuremath{\rightarrow}5p${\mathrm{}}^{2}$${\mathrm{P}}_{\mathrm{j}}$\ensuremath{\rightarrow}8s${\mathrm{}}^{2}$${\mathrm{S}}_{1\mathrm{/}2}$ two-photon, two-color polarization spectrum in atomic Rb are reported. As a result of interference between the transition amplitudes for the process, the spectrum is strongly frequency and linear polarization dependent in the vicinity of the 5s${\mathrm{}}^{2}$${\mathrm{S}}_{1\mathrm{/}2}$\ensuremath{\rightarrow}5p${\mathrm{}}^{2}$${\mathrm{P}}_{1\mathrm{/}2}$ and 5s${\mathrm{}}^{2}$${\mathrm{S}}_{1\mathrm{/}2}$\ensuremath{\rightarrow}5p${\mathrm{}}^{2}$${\mathrm{P}}_{3\mathrm{/}2}$ resonance transitions, with the linear polarization degree varying from nearly +100% to -100% over the approximate 500-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range of the data. For absorption of two collinearly polarized photons, complete destructive interference for the process occurs at a critical detuning from the 5s${\mathrm{}}^{2}$${\mathrm{S}}_{1\mathrm{/}2}$\ensuremath{\rightarrow}5p${\mathrm{}}^{2}$${\mathrm{P}}_{3\mathrm{/}2}$ resonance transition given by ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$=-155.83(3) ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The location of ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$ is determined primarily by the relative transition matrix elements through the 5p${\mathrm{}}^{2}$${\mathrm{P}}_{\mathrm{j}}$ multiplet, but also depends significantly on contributions from more energetic np${\mathrm{}}^{2}$P levels. The null in the excitation occurring at the critical frequency allows experimental determination of a type of sum rule that depends only on the atomic matrix elements and the value of ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$. Such sum rules are defined and presented for the present experiment in Rb and for a recent similar experiment in Na.

DOI
10.1103/physreva.55.3780

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An experimental investigation of the atomic-Na 3s 2^{2}2${\mathit{S}}_{1/2--}$5s 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​ two-color two-photon polarization spectrum has been made. Measurements of the linear polarization degree of the two-photon transition were made for one laser tuned within a \ifmmode\pm\else\textpm\fi{}100 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range of the atomic-Na 3p 2^{2}2Pj{\mathit{P}}_{\mathit{j}}Pj​ levels, with the second adjusted to satisfy the two-photon resonance condition. The relatively short-pulse (\ensuremath{\sim}0.5 ns) lasers used eliminate effects on the spectrum due to atomic-Na hyperfine interactions and radiation trapping, while greatly reducing depolarization due to collisions with Ar gas. In the absence of collisions, the measured polarization spectrum is in excellent agreement with calculations. Measurements of the Ar pressure dependence of the spectrum revealed strong depolarization in the vicinity of resonant excitation through the 3p 2^{2}2P3/2{\mathit{P}}_{3/2}P3/2​ level. A collisional depolarization cross section of 200(30) \AA{} for this process was deduced from the data.
Summary form only given. A number of sophisticated techniques have been applied to precise measurements of the strength of resonance transitions in heavier alkali atoms. These include refined lifetime measurements in atomic beams, photoassociative spectroscopy of cold atoms confined to atomic traps, and direct measurements of the natural width of an atomic transition. We have made a precise study of the 5s-5p-5d transition in atomic Rb. Measurements of the non-resonant two-photon, two-color linear depolarization spectrum show remarkable polarization-dependent interference structure. Using this novel approach, it was possible to extract the ratio of the transition matrix elements for the two contributing pathways.
A combined experimental and theoretical study of transition matrix elements of the $6p{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}$ transition in atomic Cs is reported. Measurements of the polarization-dependent two-photon excitation spectrum associated with the transition were made in an $\ensuremath{\approx}200{\mathrm{cm}}^{\ensuremath{-}1}$ range on the low-frequency side of the $6s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}6p{}^{2}{P}_{3/2}$ resonance. The measurements depend parametrically on the relative transition matrix elements, but also are sensitive to far-off-resonance $6s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}\mathrm{np}{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}$ transitions. In addition, as the measured quantities are ratios of polarization-dependent intensities at a single-excitation frequency, they are quite insensitive to a variety of common-mode systematic effects; matrix-element ratios may then be determined to high accuracy. In the past, the matrix-element dependence has yielded a generalized sum rule, the value of which is dependent on sums of relative two-photon transition matrix elements. In the present case, best available determinations from other experiments are combined with theoretical matrix elements to extract the ratio of transition matrix elements for the $6p{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}(j=1/2,3/2)$ transition. The resulting experimental value of 1.423(2) is in excellent agreement with the theoretical value, calculated using a relativistic all-order method, of 1.425(2).
We present in this paper results of a nonlinear optical spectroscopy approach to measurement of excited-state transition matrix elements. Recent advances in the quality of excited-state transition matrix elements have permitted renormalization of earlier measurements of transition amplitudes associated with the 5s 2 S 1/2 → 5p 2 P j → 5d 2 D 3/2 two-photon transitions in atomic 87 Rb. Previous measurements were made to high precision, but further improvement of the accuracy was limited by uncertainties in data describing the influence of energetically distant transitions. Availability of more reliable matrix elements, including relativistic all-order calculations of transition matrix elements in alkali atoms, has since significantly improved the situation. In the present paper, we show that theoretical relative transition amplitudes for the excited state 5p 2 P j → 5d 2 D 3/2 doublet (ratio = 1.098(9)) are now in excellent agreement with experiment (ratio = 1.090(6)). This result, combined with our recent work on caesium, shows that it is possible to determine relative line strengths, for transitions connecting atomic excited states, with precision previously found only in state-of-the-art measurements of alkali resonance doublets. Detailed discussion of the experimental technique and supporting data, including polarization measurements on the 5s 2 S 1/2 → 5p 2 P j → 5d 2 D 5/2 transitions, is also presented.