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arXiv:0805.2993 · Journal of the Optical Society of America B

Anomalous dispersion and negative group velocity in a coherence-free cold atomic medium

William G. A. Brown, Russell McLean, Andrei I. Sidorov, Peter Hannaford, A. M. Akulshin

Published Sep 17, 2008• 15 citations
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Abstract

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.

DOI
10.1364/josab.25.000c82

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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.
We present the results of experimental studies of the propagation of light pulses through a specially prepared atomic medium with steep anomalous dispersion and enhanced Kerr nonlinearity. The observed negative group velocity is consistent with the principle of causality. The long-lived bright Zeeman coherence that is responsible for the steep anomalous dispersion gives rise also to a giant nonlinearity of the atomic susceptibility, which contributes substantially to the pulse propagation process. The enhanced atomic Kerr nonlinearity in the bright coherent state has been estimated.
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.
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.
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].
Experimental investigation of the optical properties of atomic media with bright and dark long-lived light-induced Zeeman coherence is reported. We have obtained a small negative value for the group velocity of light pulses in Cs vapour ( V g ≃− c /6000), which agrees with direct anomalous dispersion measurements. The intensity dependent components of the refractive index of an atomic vapour with long-lived Zeeman coherence has been estimated. We have shown that such coherence can significantly enhance four-wave mixing, leading to the appearance of a multi-frequency comb-like spectrum at relatively low light intensity.
We investigate a light-pulse propagation with negative group velocity in a nonlinear coherent medium. We show that the necessary conditions for nonlinear superluminal effects to be observable are realized in a three-level $\ensuremath{\Lambda}$ system interacting with a linearly polarized laser field in the presence of a static magnetic field. The initially prepared Zeeman coherence cancels the resonant absorption of the medium almost completely, but preserves its dispersion anomalous and very high. In this medium the light pulse propagates superluminally in the sense that the peak of the transmitted pulse exits the medium before the peak of the incident pulse enters. At the same time the pulse group velocity is intensity dependent, which leads to the self-steepening of the pulse trailing edge due to the fact that the more intense parts of the pulse travel slower. This is in contrast with the shock wave generation in a nonlinear medium with normal dispersion. The predicted effect can be easily observed in the well-known schemes employed in the studies of nonlinear magneto-optical rotation. The upper bound of sample length is found from the criterion that the pulse self-steepening and group-advance time are observable without pulse distortion caused by the group-velocity dispersion.