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Physical Review A

Electric-field modification of two-photon, two-color, quadrupole-dipole depolarization spectra in atomic Cs

B. V. Dobrydnev, Mark D. Havey

Published Nov 1, 1996• 2 citations
Publisher

Abstract

An earlier study of the 6s${\mathrm{}}^{2}$${\mathit{S}}_{1/2}$\ensuremath{\rightarrow}5d${\mathrm{}}^{2}$${\mathit{D}}_{\mathit{j}}$\ensuremath{\rightarrow}11p${\mathrm{}}^{2}$${\mathit{P}}_{3/2}$ two-photon, dipole-quadrupole transition in Cs is extended by including the effect of an external static electric field. The dependence of the absorption spectrum on the relative polarizations of the two light sources is found to be greatly modified by a moderately sized electric field, the predominant effect being mixing of the resonant 6p${\mathrm{}}^{2}$${\mathit{P}}_{\mathit{j}}$ levels into the ground 6s${\mathrm{}}^{2}$${\mathit{S}}_{1/2}$ level. Compact theoretical expressions, parametrized in terms of the electric-field strength and the relative transition matrix elements through the 5d${\mathrm{}}^{2}$${\mathit{D}}_{\mathit{j}}$ multiplet levels, are given. Results are presented for the electric-field dependence of a linear depolarization ratio, which is very sensitive to these quantities. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.4327

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Physical Review A•Jan 1, 1997•9 citations
An earlier study of the 6s{\mathrm{}}^{2}$${\mathit{S}}_{1/2}\ensuremath{\rightarrow}5d{\mathrm{}}^{2}$${\mathit{D}}_{\mathit{j}}\ensuremath{\rightarrow}11p{\mathrm{}}^{2}$${\mathit{P}}_{3/2} two-photon, dipole-quadrupole transition in Cs is extended by including the effect of an external static electric field. The dependence of the absorption spectrum on the relative polarizations of the two light sources is found to be greatly modified by a moderately sized electric field, the predominant effect being mixing of the resonant 6p{\mathrm{}}^{2}$${\mathit{P}}_{\mathit{j}} levels into the ground 6s{\mathrm{}}^{2}$${\mathit{S}}_{1/2} level. Compact theoretical expressions, parametrized in terms of the electric-field strength and the relative transition matrix elements through the 5d{\mathrm{}}^{2}$${\mathit{D}}_{\mathit{j}} multiplet levels, are given. Results are presented for the electric-field dependence of a linear depolarization ratio, which is very sensitive to these quantities. \textcopyright{} 1996 The American Physical Society.
Results of a theoretical investigation of two-photon, two-color excitation and linear depolarization spectra in atomic cesium are presented. The case of two-beam excitation, where one photon is absorbed through a quadrupole amplitude and the other through a dipole amplitude, is considered. When excitation is through a spin multiplet, the final-state population produced depends sensitively on the relative transition amplitudes through the nondengenerate spin-multiplet terms. In addition, the transition rate contains interference terms depending on the relative directions of the two beams. These terms are manifested strongly when the intermediate states are nonresonant and when the two beams have approximately the same frequency. Application of the results to the 6s2{\mathrm{}}^{2}2S1/2{\mathit{S}}_{1/2}S1/2​\ensuremath{\rightarrow}5d2{\mathrm{}}^{2}2Dj{\mathit{D}}_{\mathit{j}}Dj​\ensuremath{\rightarrow}11p2{\mathrm{}}^{2}2P3/2{\mathit{P}}_{3/2}P3/2​, quadrupole-dipole transition in atomic Cs is made. Polarization-dependent excitation spectra are presented for this case. Effects of hyperfine interactions are also considered.
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 report a measurement of the ratio of electric dipole transition matrix elements of cesium for the $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ transitions. We determine this ratio of matrix elements through comparisons of two-color, two-photon excitation rates of the 7s2S1/27s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}7s2S1/2​ state using laser beams with polarizations parallel to one another vs perpendicular to one another. Our result of $R\ensuremath{\equiv}\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}/\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=1.5272(17)$ is in excellent agreement with a theoretical prediction of R=1.5270(27)R=1.5270(27)R=1.5270(27). Moreover, the accuracy of the experimental ratio is sufficiently high to differentiate between various theoretical approaches. To our knowledge, there are no prior experimental measurements of RRR. Combined with our recent determination of the lifetime of the 7s2S1/27s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}7s2S1/2​ state, we determine reduced matrix elements for these two transitions, $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}=\ensuremath{-}6.489(5)\phantom{\rule{4pt}{0ex}}{a}_{0}$ and $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=\ensuremath{-}4.249(4)\phantom{\rule{4pt}{0ex}}{a}_{0}$. These matrix elements are also in excellent agreement with theoretical calculations. These measurements improve knowledge of Cs properties needed for parity violation studies and provide benchmarks for tests of high-precision theory.
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.
Measurements of the linear polarization degree of the $5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{{j}^{\ensuremath{'}}}$ transitions ${(j}^{\ensuremath{'}}=1/2,3/2)$ in atomic 87Rb{}^{87}\mathrm{Rb}87Rb are reported. The radiative transitions are electric-dipole forbidden, but electric-quadrupole allowed. In addition, because of the relatively strong spin-orbit interaction in Rb, the $p\ensuremath{-}p$ transitions can acquire a magnetic-dipole transition strength that may be a measurable fraction of the electric-quadrupole strength. The polarization measurements can generally provide a different and sensitive way to extract the relative transition strengths. We have measured the linear polarization degree of the $5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{{j}^{\ensuremath{'}}}$ transitions over a wide range of Rb density. We report here observations of a different depolarization effect, whereby the measured polarization of the $5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{1/2}$ transition increases, while that for the $5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{3/2}$ transition decreases with increasing Rb density. The behavior is attributed to strong laser field effects associated with the $5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}$ resonance transition.
Precise measurements are reported on the linear polarization spectrum associated with two-photon, two-color spectroscopy of the 3 s2{\mathrm{s}}^{2}s2 S1/2{\mathrm{S}}_{1\mathrm{/}2}S1/2​ \ensuremath{\rightarrow}5 s2{\mathrm{s}}^{2}s2 S1/2{\mathrm{S}}_{1\mathrm{/}2}S1/2​ transition in atomic Na. Measurements are made in an approximately 40-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range in the vicinity of the 3 p2{\mathrm{p}}^{2}p2 Pj{\mathrm{P}}_{\mathrm{j}}Pj​ (j=1/2,3/2) levels, which serve as the principal intermediate levels for the two-photon transitions. Because of interference between the transition amplitudes through each fine-structure multiplet component, the polarization varies from nearly 100% to -100% within this spectral range. Modeling the data to include the effects of more energetic p levels and allowing for a j-dependent ratio of transition amplitudes R results in an excellent fit to the data. Estimation of the contribution of higher p levels allows extraction of a value and sign for R=+1.0012(12). This result is combined with recent measurements of the lifetime of the resonance transitions in Na to obtain a value for the ratio of excited-state transition-matrix elements for the 3 p2{\mathrm{p}}^{2}p2 Pj{\mathrm{P}}_{\mathrm{j}}Pj​ \ensuremath{\rightarrow}5 s2{\mathrm{s}}^{2}s2 S1/2{\mathrm{S}}_{1\mathrm{/}2}S1/2​ transition (j=3/2 compared to j=1/2) of 1.0013(15).