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arXiv:quant-ph/9906019 · Physical Review Letters

Steep Anomalous Dispersion in Coherently Prepared Rb Vapor

A. M. Akulshin, S. Barreiro, A. Lezama

Published Nov 22, 1999• 163 citations
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Abstract

Steep dispersion of opposite signs in driven degenerate two-level atomic transitions have been predicted and observed on the ${D}_{2}$ line of ${}^{87}\mathrm{Rb}$ in an optically thin vapor cell. The intensity dependence of the anomalous dispersion has been studied. The maximum observed value of anomalous dispersion ( $\mathrm{dn}/d\ensuremath{\nu}\ensuremath{\simeq}\ensuremath{-}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}{\mathrm{Hz}}^{\ensuremath{-}1}$) corresponds to a negative group velocity ${V}_{g}\ensuremath{\simeq}\ensuremath{-}c/23000$.

DOI
10.1103/physrevlett.83.4277

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Steep dispersion of opposite signs in driven degenerate two-level atomic transitions have been predicted and observed on the D2{D}_{2}D2​ line of 87Rb{}^{87}\mathrm{Rb}87Rb in an optically thin vapor cell. The intensity dependence of the anomalous dispersion has been studied. The maximum observed value of anomalous dispersion ( dn/d\ensuremathν\ensuremath≃\ensuremath−6\ifmmode×\else\texttimes\fi10\ensuremath−11Hz\ensuremath−1\mathrm{dn}/d\ensuremath{\nu}\ensuremath{\simeq}\ensuremath{-}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}{\mathrm{Hz}}^{\ensuremath{-}1}dn/d\ensuremathν\ensuremath≃\ensuremath−6\ifmmode×\else\texttimes\fi10\ensuremath−11Hz\ensuremath−1) corresponds to a negative group velocity Vg\ensuremath≃\ensuremath−c/23000{V}_{g}\ensuremath{\simeq}\ensuremath{-}c/23000Vg​\ensuremath≃\ensuremath−c/23000.
Summary form only given. The propagation of light in a dispersive medium is characterized by the group velocity /spl nu//sub g/=c(n+/spl nu//sup dn//d/spl nu/)/sup .1/ where n is the refractive index and /spl nu/ the optical frequency. Depending on the sign and magnitude of /sup dn//d/spl nu/ in the medium, the group velocity can be positive, infinite or negative. The group velocity corresponds to the speed of the propagation of the maximum of an optical pulse travelling into the medium. This remains true whether the dispersion in the medium is normal (/sup dn//d/spl nu/>0) or anomalous (/sup dn//d/spl nu/<0). It has been demonstrated that coherently prepared atomic systems can exhibit steep dispersion leading to small absolute values of the group velocity (slow light). In recent work, we have demonstrated that narrow resonances arising from the coherent interaction of two optical fields with a closed atomic transition between two degenerate levels may correspond to a steep anomalous dispersion and thus to slow and negative group velocity. We report on the experimental study of the propagation of an amplitude modulated wave in a medium presenting negative group velocity.
We compare the behavior of absorption and of resonance fluorescence spectra in an extremely thin Rb vapor cell as a function of the ratio of $L∕\ensuremath{\lambda}$, with LLL the cell thickness $(L\ensuremath{\sim}150--1800\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ and $\ensuremath{\lambda}$ the wavelength of the Rb D2{D}_{2}D2​ line $(\ensuremath{\lambda}=780\phantom{\rule{0.3em}{0ex}}\mathrm{mn})$. The Dicke-type coherent narrowing [G. Dutier et al., Europhys. Lett. 63, 35 (2003)] is observed only in transmission measurements, in the linear regime, with its typical collapse and revival, which reaches a maximum for $L=(2n+1)\ensuremath{\lambda}∕2$ (nnn integer). It is shown not to appear in fluorescence, whose behavior-amplitude, and spectral width, is more monotonic with LLL. Conversely, at high-intensity, the sub-Doppler saturation effects are shown to be the most visible in transmission around $L=n\ensuremath{\lambda}$.
We have measured the index of refraction in the region of a coherent population trapping resonance in a cesium vapor cell with an interferometric technique. We find very high normal dispersion (up to $\frac{\mathrm{dn}}{\mathrm{df}}=9.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ ${\mathrm{Hz}}^{\ensuremath{-}1}$) at low absorption. From our spectra we obtain very small group velocities below c3000\frac{c}{3000}3000c​. This corresponds to a delay time of more than 200 ns for a cesium cell 20 mm in length, equivalent to more than 60 m of propagation in vacuum.
A large increase in atomic absorption due to coherent interaction with resonant radiation is predicted for a closed transition between two degenerate atomic levels verifying 0<Fg<Fe(Fg0<{F}_{g}<{F}_{e}{(F}_{g}0<Fg​<Fe​(Fg​ and Fe{F}_{e}Fe​ are the total angular momentum of the ground and the excited levels, respectively). In good agreement with the theoretical prediction, a total absorption enhancement by a factor 1.7 was obtained on the D2{D}_{2}D2​ line of 85Rb{}^{85}\mathrm{Rb}\mathrm{}85Rb in a vapor cell experiment.