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Physical Review A

Selective reflection by Rb

Ping Wang, A. Gallagher, J. Cooper

Published Aug 1, 1997• 39 citations
Publisher

Abstract

Perpendicular reflection of low-power, near-resonant radiation at a sapphire--Rb-vapor interface (selective reflection) has been measured for Rb densities of $3\ifmmode\times\else\texttimes\fi{}{10}^{14}--3\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. At the lowest density the eight hyperfine components are essentially isolated, and at the highest pressure they are highly blended. The data have been fitted to a coherent superposition of the reflected field amplitudes of the eight components, including the well-known starting transient and wall interaction. At low to moderate densities this yields a good fit to the data, and a result for the Rb-Rb collisional shift. At the higher densities the rapid attenuation of the incident field has a major effect on the reflection spectrum, and an approximation to this is included in the calculation, assuming exponential attenuation at the equilibrium-vapor rate. This provides improved fits to the data and allows the apparent Lorentz-Lorenz plus collisional shift to be evaluated. However, the data do not fully fit this calculation, and a complete self-consistent-field calculation appears necessary to fully understand the high-pressure results.

DOI
10.1103/physreva.56.1598

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A theory of selective reflection (SR) of a light beam from the interface of a dielectric medium and a dense atomic vapor is presented. Following another earlier work on this subject [J. Guo et al., Opt. Commun. 110, 732 (1994)], we calculate the atomic density matrix and the transmitted field in the vapor self-consistently. We extend our previous theory to include an attractive atom-dielectric wall interaction and multiple atomic transitions. We examine the limits at which the conventional SR theories, which are based on the assumption of a plane-wave field in the vapor, start to fail. It is shown that at or above vapor densities of order ${10}^{17}$/${\mathrm{cm}}^{3}$, the frequency shifts of the SR line shape due to the local-field correction (Lorentz-Lorenz shift), the atom-wall interaction, and the nonexponential attenuation of the field in the vapor can have comparable orders of magnitude, and the proper determination of all these effects is essential for calculating the correct SR signals. A comparison of the theoretical SR spectra with an experimental result for a Rb vapor with a density of order ${10}^{17}$/${\mathrm{cm}}^{3}$ is also presented. \textcopyright{} 1996 The American Physical Society.

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Rb気体の選択反射信号の尖鋭化

Taro ITO

The selective reflection spectra of Rb D_1 line from a glass vapor interface has been studied as a function of incidence angles of light. It has been observed that the Doppler broadning of the spectra has been partially reduced for the nearly normal incidence of light to the interface, and that the 85Rb hyperfine structure of the excited state 2P_1/2, which is usually masked in the Doppler width, has been almost resolved as a result of the spectral narrowing. The observed line shapes are in good agreement with the theoretical ones including the effect of atom-wall collision.|Rb D_1線の境界面からの選択反射スペクトルが入射光角度の関数として調べられた。スペクトルのドップラー広がりが、境界面への垂直入射光に対して部分的に減少し、ドップラー幅に埋没している85Rbの励起状態2P_1/2の超微細構造が、このスペクトル尖鋭化の結果、ほとんど分解されるのが観測された。観測されたスペクトル線の形は原子と壁との衝突の効果を考慮した理論によるスペクトル線の形と良く一致している。

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Lorentz red shift and self-broadening of atomic potassium vapor

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The Lorentz-Lorenz equation predicts that the dispersion feature of an isolated optical resonance should have a density-dependent frequency shift toward the red end of the spectrum. We have investigated the dispersion feature experimentally by observing the frequency dependence of the Fresnel reflection (selective reflection) from the boundary between a dense atomic potassium vapor and the window of the vessel containing the vapor. We find that the selective-reflection features of both the S1/2-P1/2 (770.1 nm) and S1/2-P3/2 (766.7 nm) lines of potassium shift increasingly toward the red and broaden as the number density of the vapor is increased to 2 × 1017 atoms/cm3. We compare the results of the experiment to theoretical predictions for the selective reflection. The broadening is well described by conventional binary collision theory; however, the observed red shift of both of the lines is somewhat larger than that predicted by the Lorentz-Lorenz equation. It is possible that other mechanisms that lead to frequency shifts are occurring.

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High resolution selective reflection spectroscopy as a probe of long-range surface interaction : measurement of the surface van der Waals attraction exerted on excited Cs atoms

Martine Chevrollier, Mich�le Fichet, Marcos Oriá +3 more

Selective reflection spectroscopy at an interface with a low-density resonant vapor, especially when combined with a frequency modulation technique, is a high-resolution Doppler-free tool for probing atoms interacting with a surface. We analyze different types of relevant surface interaction, emphasizing the spectral consequences of a van der Waals surface attraction associated to a $z^{-3}$ potential dependence ($z$: distance to the wall). We present detailed results of two series of experiments at a Cs vapor/dielectric window interface on the 6S$_{1/2}$-6P$_{3/2}$ ($\lambda = 852$ nm) resonance line and on the 6S$_{1/2}$-7P second resonance line ($\lambda = 455$ nm and 459 nm). Lineshape analysis at various pressures consistently shows that a van der Waals-type surface attraction has to be considered to interpret strong lineshape distortions and resonance shift. The attractive strengths are found to be equal respectively to $\approx 2$ kHz $\mu$m$^3$ and $\approx 20$ kHz $\mu$m$^3$, independently of the considered hyperfine component, within the experimental accuracy. It yields also typical parameters of pressure broadening and shift, which are shown to originate in collisional processes, at densities where the medium is opaque. Theoretical expectations for the VW strength are discussed on the basis of the results of atomic theory. The predicted values are smaller, by a typical factor of 2, than those deduced from the experiments. The validity of the theory, when applied to a dielectric interface, is discussed and seems questionable when the frequency of virtual atomic transitions involved in the van der Waals attraction potential lies in the dielectric window absorption range.

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Attenuated Total Reflection Signals from Rb Vapor

Taro ITO, 三宅, 宏司

Attenuated total reflection(ATR)signals have been studied at an interface between Rb vapor and a glass using the Rb D_1 line.Resonance line shapes,amplitudes and linewidths have been observed to undergo remarkable changes for incidences of light near the critical angle.These experimental results have been found to agree well with the predictions of the conventional electromagnetic theory of light.|Rb気体とガラスの境界面における全反射減衰信号が,RbのD_1線を用いて調べられた。共鳴の線形や振幅および線幅が,臨界角近傍での入射光に対し,著しく変化するのが観測された。これらの実験結果は,光の電磁波理論から予測される事柄と良く一致することが見いだされた。

•Feb 28, 1993•0 citations
Perpendicular reflection of low-power, near-resonant radiation at a sapphire--Rb-vapor interface (selective reflection) has been measured for Rb densities of 3\ifmmode×\else\texttimes\fi1014−−3\ifmmode×\else\texttimes\fi1017/cm33\ifmmode\times\else\texttimes\fi{}{10}^{14}--3\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}3\ifmmode×\else\texttimes\fi1014−−3\ifmmode×\else\texttimes\fi1017/cm3. At the lowest density the eight hyperfine components are essentially isolated, and at the highest pressure they are highly blended. The data have been fitted to a coherent superposition of the reflected field amplitudes of the eight components, including the well-known starting transient and wall interaction. At low to moderate densities this yields a good fit to the data, and a result for the Rb-Rb collisional shift. At the higher densities the rapid attenuation of the incident field has a major effect on the reflection spectrum, and an approximation to this is included in the calculation, assuming exponential attenuation at the equilibrium-vapor rate. This provides improved fits to the data and allows the apparent Lorentz-Lorenz plus collisional shift to be evaluated. However, the data do not fully fit this calculation, and a complete self-consistent-field calculation appears necessary to fully understand the high-pressure results.
A theory of selective reflection (SR) of a light beam from the interface of a dielectric medium and a dense atomic vapor is presented. Following another earlier work on this subject [J. Guo et al., Opt. Commun. 110, 732 (1994)], we calculate the atomic density matrix and the transmitted field in the vapor self-consistently. We extend our previous theory to include an attractive atom-dielectric wall interaction and multiple atomic transitions. We examine the limits at which the conventional SR theories, which are based on the assumption of a plane-wave field in the vapor, start to fail. It is shown that at or above vapor densities of order 1017{10}^{17}1017/cm3{\mathrm{cm}}^{3}cm3, the frequency shifts of the SR line shape due to the local-field correction (Lorentz-Lorenz shift), the atom-wall interaction, and the nonexponential attenuation of the field in the vapor can have comparable orders of magnitude, and the proper determination of all these effects is essential for calculating the correct SR signals. A comparison of the theoretical SR spectra with an experimental result for a Rb vapor with a density of order 1017{10}^{17}1017/cm3{\mathrm{cm}}^{3}cm3 is also presented. \textcopyright{} 1996 The American Physical Society.
We have observed attenuated total reflection at a glass/rubidium vapor interface in high precision. The atom density was from $3.8\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}3.7\ifmmode\times\else\texttimes\fi{}{10}^{21}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{\ensuremath{-}3}$ and the angle of incidence was from 48.4 to 64.8\ifmmode^\circ\else\textdegree\fi{}. Redshift and broadening of the reflection spectra were observed. The redshift depended on atom density, angle of incidence, light polarization and hyperfine structure. The observed broadening was attributed to the self-broadening of the resonance line. Calculation based on the Fresnel formula with a local index for the susceptibility of the vapor, which included the Lorentz local field correction and the modification of the wave vector of the evanescent light by the optically dense atomic vapor, was found to be in reasonable agreement with the experimental results.
The selective reflection spectra of Rb D_1 line from a glass vapor interface has been studied as a function of incidence angles of light. It has been observed that the Doppler broadning of the spectra has been partially reduced for the nearly normal incidence of light to the interface, and that the 85Rb hyperfine structure of the excited state 2P_1/2, which is usually masked in the Doppler width, has been almost resolved as a result of the spectral narrowing. The observed line shapes are in good agreement with the theoretical ones including the effect of atom-wall collision.|Rb D_1線の境界面からの選択反射スペクトルが入射光角度の関数として調べられた。スペクトルのドップラー広がりが、境界面への垂直入射光に対して部分的に減少し、ドップラー幅に埋没している85Rbの励起状態2P_1/2の超微細構造が、このスペクトル尖鋭化の結果、ほとんど分解されるのが観測された。観測されたスペクトル線の形は原子と壁との衝突の効果を考慮した理論によるスペクトル線の形と良く一致している。
The Lorentz-Lorenz equation predicts that the dispersion feature of an isolated optical resonance should have a density-dependent frequency shift toward the red end of the spectrum. We have investigated the dispersion feature experimentally by observing the frequency dependence of the Fresnel reflection (selective reflection) from the boundary between a dense atomic potassium vapor and the window of the vessel containing the vapor. We find that the selective-reflection features of both the S1/2-P1/2 (770.1 nm) and S1/2-P3/2 (766.7 nm) lines of potassium shift increasingly toward the red and broaden as the number density of the vapor is increased to 2 × 1017 atoms/cm3. We compare the results of the experiment to theoretical predictions for the selective reflection. The broadening is well described by conventional binary collision theory; however, the observed red shift of both of the lines is somewhat larger than that predicted by the Lorentz-Lorenz equation. It is possible that other mechanisms that lead to frequency shifts are occurring.
Selective reflection spectroscopy at an interface with a low-density resonant vapor, especially when combined with a frequency modulation technique, is a high-resolution Doppler-free tool for probing atoms interacting with a surface. We analyze different types of relevant surface interaction, emphasizing the spectral consequences of a van der Waals surface attraction associated to a z−3z^{-3}z−3 potential dependence (zzz: distance to the wall). We present detailed results of two series of experiments at a Cs vapor/dielectric window interface on the 6S1/2_{1/2}1/2​-6P3/2_{3/2}3/2​ (λ=852\lambda = 852λ=852 nm) resonance line and on the 6S1/2_{1/2}1/2​-7P second resonance line (λ=455\lambda = 455λ=455 nm and 459 nm). Lineshape analysis at various pressures consistently shows that a van der Waals-type surface attraction has to be considered to interpret strong lineshape distortions and resonance shift. The attractive strengths are found to be equal respectively to ≈2\approx 2≈2 kHz μ\muμm3^33 and ≈20\approx 20≈20 kHz μ\muμm3^33, independently of the considered hyperfine component, within the experimental accuracy. It yields also typical parameters of pressure broadening and shift, which are shown to originate in collisional processes, at densities where the medium is opaque. Theoretical expectations for the VW strength are discussed on the basis of the results of atomic theory. The predicted values are smaller, by a typical factor of 2, than those deduced from the experiments. The validity of the theory, when applied to a dielectric interface, is discussed and seems questionable when the frequency of virtual atomic transitions involved in the van der Waals attraction potential lies in the dielectric window absorption range.
Attenuated total reflection(ATR)signals have been studied at an interface between Rb vapor and a glass using the Rb D_1 line.Resonance line shapes,amplitudes and linewidths have been observed to undergo remarkable changes for incidences of light near the critical angle.These experimental results have been found to agree well with the predictions of the conventional electromagnetic theory of light.|Rb気体とガラスの境界面における全反射減衰信号が,RbのD_1線を用いて調べられた。共鳴の線形や振幅および線幅が,臨界角近傍での入射光に対し,著しく変化するのが観測された。これらの実験結果は,光の電磁波理論から予測される事柄と良く一致することが見いだされた。