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Physical Review A

Steep dispersion and group velocity below c3000 in coherent population trapping

Oliver G. Schmidt, R. Wynands, Z. Hussein, Dieter Meschede

Published Jan 1, 1996• 195 citations
Publisher

Abstract

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 $\frac{c}{3000}$. 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.

DOI
10.1103/physreva.53.r27

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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 dndf=9.7\ifmmode×\else\texttimes\fi10\ensuremath−12\frac{\mathrm{dn}}{\mathrm{df}}=9.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}dfdn​=9.7\ifmmode×\else\texttimes\fi10\ensuremath−12 Hz\ensuremath−1{\mathrm{Hz}}^{\ensuremath{-}1}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.
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 investigate the reduction of the group velocity propagation resulting from the steep change of the refractive index by the coherent population oscillation in erbium-doped optical fibre. The largest delay is measured to be about 8.75ms corresponding to a group index of 1.312 × 10 6 . The time delay or advancement depends on the pump intensity. Influences of the ion density on the fractional delay and the group velocity reduction of light propagation are studied. Based on our discussion the optimization parameters should be selected in order to obtain more appropriate time delay and the slowdown of group velocity.
An atomic transition that has been made transparent by applying an additional electromagnetic field exhibits a rapidly varying refractive index with zero group velocity dispersion at line center. A 10-cm-long Pb vapor cell at an atom density of 7\ifmmode\times\else\texttimes\fi{}1015{10}^{15}1015 atoms/cm3{\mathrm{cm}}^{3}cm3 and probed on its 283-nm resonance transition has a calculated optical delay of 83 ns [(c/VG{\mathit{V}}_{\mathit{G}}VG​)=250].
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 ( $\mathrm{dn}/d\ensuremath{\nu}\ensuremath{\simeq}\ensuremath{-}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}{\mathrm{Hz}}^{\ensuremath{-}1}$) corresponds to a negative group velocity ${V}_{g}\ensuremath{\simeq}\ensuremath{-}c/23000$.
We studied experimentally the influence of thermal atomic motion on light propagation in a vacuum atomic vapour cell above room temperature. We found that atomic motion introduces sizable changes in the spectral properties of the medium, such as dispersion and absorption, if the conditions for coherent population trapping are fulfilled. In particular, studying the group delay of light in the atomic vapour, we confirm the theoretical predictions of Kocharovskaya et al. (2001, Phys. Rev. Lett., 86, 628) and demonstrate that a coherent atomic medium has light dragging abilities large enough to make feasible the realization of frozen light based on atomic motion. We also demonstrate that dragging can be observed in measurements of the electromagnetically induced transparency resonance width, as well as in group delay measurements.