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Physical Review A

Probing the spatial dispersion in a dense atomic vapor near a dielectric interface

H. van Kampen, Vladimir A. Sautenkov, E. R. Eliel, J. P. Woerdman

Published Dec 1, 1998• 12 citations
Publisher

Abstract

We have experimentally investigated the selective reflection of the $P\ensuremath{-}D$ transition in a high-density rubidium vapor and shown it to be sensitive to the exact spatial distribution of $P$-state atoms near the dielectric-vapor interface. This distribution results from the radiative and nonradiative transport of excitation and from wall-quenching collisions of excited-state atoms and is highly inhomogeneous. Selective reflection thus acts as a probe of the spatial dispersion in the vapor. The resulting spectra have been analyzed to show that the broadening due to $S\ensuremath{-}D$ collisions contributes considerably to the self-broadened linewidth of the $P\ensuremath{-}D$ transition.

DOI
10.1103/physreva.58.4473

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We have experimentally investigated the selective reflection of the P\ensuremath−DP\ensuremath{-}DP\ensuremath−D transition in a high-density rubidium vapor and shown it to be sensitive to the exact spatial distribution of PPP-state atoms near the dielectric-vapor interface. This distribution results from the radiative and nonradiative transport of excitation and from wall-quenching collisions of excited-state atoms and is highly inhomogeneous. Selective reflection thus acts as a probe of the spatial dispersion in the vapor. The resulting spectra have been analyzed to show that the broadening due to S\ensuremath−DS\ensuremath{-}DS\ensuremath−D collisions contributes considerably to the self-broadened linewidth of the P\ensuremath−DP\ensuremath{-}DP\ensuremath−D transition.
We study the frequency derivatives of selective reflection from high-density rubidium vapor using a hole-burning technique. Saturation dips are observed inside the self-broadened line shapes. The line self-broadening is a combination of static width and collision width. By analyzing saturation dips, we can separate power broadening and collision width. Our experimental results support the theory of inhomogeneous dipole-dipole induced broadening of transitions in a dense atomic gas, published by J. A. Leegwater and S. Mukamel [Phys. Rev. A 49 (1994) 146].
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.
We calculate the reflection coefficient for a light beam incident on the interface between a dielectric and a resonant atomic vapor to first order in the dipole polarization in the vapor. The angle of incidence and the polarization direction are chosen arbitrarily, and saturation is fully accounted for. The atoms are supposed to get deexcited at collisions with the surface. The resulting transient behavior of atoms leaving the surface is responsible for a nonlocal response. This spatial dispersion near the surface is known to produce a natural-linewidth-limited resonance in the vapor reflection coefficient at normal incidence. Our analysis shows that this sub-Doppler structure is broadened by the residual Doppler effect for non-normal incidence. This structure disappears at the critical angle for total internal reflection, where one predicts a conventional Voigt-type dispersion response, based on the complex-refractive-index approach. We also calculate the saturation broadening of the atomic response for large intensities. Beyond the critical angle, the spectral response suddenly shifts from dispersion to absorption line shapes. In the case of total internal reflection, the spatial dispersion leads to an additional Lorentzian broadening, which results from an effective imaginary Doppler shift at passage through the evanescent wave (transit-time broadening).
The dipole–dipole broadening of the spectrum of the selective reflection of intense resonance light from the interface between a transparent dielectric and a gas of the natural mixture of Rb isotopes has been studied experimentally. The case of a high gas density where the Doppler broadening can be neglected has been investigated. It has been shown that dipole–dipole broadening is reduced with increasing the number density of excited atoms. When the laser beam intensity is much higher than the saturation intensity of a resonance transition, a significant broadening due to the very high laser beam intensity has not been observed in the reflection spectrum from the transparent dielectric/gas interface. The observed intensity dependence of the spectral width has been explained by the quenching collisions of the excited atoms with the interface.
A nonlinear selective reflection from the boundary between a transparent dielectric and dense Rb vapor has been investigated, where the dipole broadening of the 5 S 1/2 –5 P 3/2 working transition is significantly larger than the contribution of the Doppler width. A tunable probe laser and a pump laser with a fixed frequency have been used in the experiment. At a high intensity of pump radiation, a dip has appeared in the reflection spectrum, which splits the spectrum into two symmetric resonances. The splitting value is twice the Rabi frequency. The observation of a narrow structure corresponding to the dressed atomic states opens up additional possibilities for the study of many-particle interactions.