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Quantum Electronics

Negative group velocity of a light pulse in cesium vapour

A. M. Akulshin, Alberto Cimmino, G. I. Opat

Published Jul 31, 2002• 41 citations
Publisher

Abstract

Electromagnetically induced absorption in cesium vapour causes an extremely strong anomalous dispersion, leading to the propagation of radiation at a low negative group velocity V g . As a result, a resonance light pulse appears from the medium before than a nonresonance pulse. The advance time measured in the experiment corresponds to the group velocity V g ≈ - c /3600, which is an order of magnitude lower than that reported by Wang L.J., et al. Nature, 406 , 277 (2000).

DOI
10.1070/qe2002v032n07abeh002249

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Quantum Electronics and Laser Science Conference•Nov 13, 2002•1 citation
Electromagnetically induced absorption in cesium vapour causes an extremely strong anomalous dispersion, leading to the propagation of radiation at a low negative group velocity V g . As a result, a resonance light pulse appears from the medium before than a nonresonance pulse. The advance time measured in the experiment corresponds to the group velocity V g ≈ - c /3600, which is an order of magnitude lower than that reported by Wang L.J., et al. Nature, 406 , 277 (2000).
The mechanisms leading to a seemingly superluminal propagation of light in dispersive media are examined. The anomalous dispersion near an absorption line, involved in the first experiments displaying negative group velocity propagation, is shown to be not only simpler but also more efficient than the so-called transparent dispersion used in the later experiments of Wang et al. (Nature (London) 406, 277 (2000)) and of Dogariu et al. (Phys.Rev.A 63, 053806 (2001)). The modest pulse advances observed by these authors can in particular be reproduced with a better overall transmittance of the medium and the significant advances attained with a single-line arrangement would probably be unattainable with their gain-doublet arrangement.
We have observed the propagation of an approximately 35 ns long light pulse with a negative group velocity through a laser-cooled 85Rb atomic medium. The anomalous dispersion results from linear atom–light interaction and is unrelated to long-lived ground-state coherences often associated with fast light in atomic media. The observed negative group velocity (−c/360) in the Rb magneto-optical trap for a pulse attenuated by less than 50% is in good agreement with the value of dispersion measured independently by a rf heterodyne method. The spectral region of anomalous dispersion is between 15 and 40 MHz, which is an order of magnitude wider than that typically associated with ground-state coherences.
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.
The existence of anomalous, i.e. superluminal or negative, group velocities [1] provides one of the most amazing phenomenon of wave propagation which is compatible with, and even a consequence of, causality [2]. Anomalous wave propagation generally relies on the resonant interaction of light with an atomic medium, i.e. it exploits the dispersive properties of absorptive [3] or inverted [4,5] atomic media near resonances. Evanescent wave propagation across photonic barriers [1] provides the other wide framework where anomalous group velocities have been observed, however in such cases the achievement of a negative group velocity seems unlikely. By exploiting the dispersive properties of a gain doublet, a narrow spectral region of transparent anomalous dispersion around the dip center of two Lorentzian gain lines, leading to negative transit times and no pulse attenuation, can be created [4]. A recent demonstration thereof has been indeed reported in an experiment by Wang and coworkers using Cs vapor [5].
Anomalous dispersion cannot occur in a transparent passive medium where electromagnetic radiation is being absorbed at all frequencies, as pointed out by Landau and Lifshitz. Here we show, both theoretically and experimentally, that transparent linear anomalous dispersion can occur when a gain doublet is present. Therefore, a superluminal light-pulse propagation can be observed even at a negative 7group velocity through a transparent medium with almost no pulse distortion. Consequently, a negative transit time is experimentally observed resulting in the peak of the incident light pulse to exit the medium even before entering it. This counterintuitive effect is a direct result of the rephasing process owing to the wave nature of light and is not at odds with either causality or Einstein's theory of special relativity.
Summary form only given. We use gain-assisted linear anomalous dispersion to demonstrate superluminal light pulse propagation with a negative group velocity through a transparent atomic medium. We place two Raman gain peaks closely to obtain an essentially lossless anomalous dispersion region that results in a superluminal group velocity. The group velocity of a pulse in this region exceeds c and can even become negative,while the shape of the pulse is preserved. We measured a negative group velocity index of n/sub g/=-315(/spl plusmn/5). Experimentally, a light pulse propagating through the spin-polarized atomic vapor cell exits from it earlier than propagating through the same distance in vacuum by a time difference that is 315 times of the vacuum light propagation time L/c=0.2 ns.