content_image/312355.jpg
the broadening due to absorption and dispersion if we assume that the pulse is centered at the center of gravity of the transitions, s 1 = s 2 , and γ 1 = γ 2 = γ [11, 21]. Following the approach taken by Boyd et al. in Ref. [11], we set the pulse broadening caused by each mechanism equal to a fixed value (here we choose f$_{B}$ = 1) and calculate the length of the slow light medium required to produce that amount of broadening. We find that 

<img src='content_image/312355.jpg'>

where L$_{A,D}$ are the required path lengths for the absorptive and dispersion contributions and ω 21 = ( ω 2 − ω 1 ) / 2 is half of the separation between the centers of the resonances. Absorptive broadening is larger than (smaller than) dispersive broadening for L$_{A}$/L$_{D}$ > 1 ( L$_{A}$/L$_{D}$ < 1). In general, the relative importance of absorption and dispersion depends both on the pulse width and resonance line separation normalized by the resonance linewidth. For the case where ω 21 /γ >> 1 (which is the case for the atomic resonances studied in this paper), Eq. 3 reduces to L$_{A}$/L$_{D}$ ∼ 1 / 2 γT 0 and depends only on the pulse width relative to the atomic linewidth. Thus, as T 0 >> γ for all of the experiments reported in this paper, dispersion is the dominant broadening mechanism. 

## References 

1. R.W. Boyd and D. J. Gauthier, “‘Slow’ and ‘Fast’ Light,” Progress in Optics, Vol. 43, E. Wolf, Ed. (Elsevier, Amsterdam, 2002), Ch. 6, pp. 497-530. 

2. R. W. Boyd and D. J. Gauthier, “Controlling the Velocity of Light Pulses,” Science 326 , 1074 (2009). 

3. C.J. Broadbent, R.M. Camacho, R. Xin, and J.C. Howell, “Preservation of Energy-Time Entanglement in a Slow Light Medium,” Phys. Rev. Lett. 100 , 133602 (2008). 

4. M.D. Stenner, D.J. Gauthier, and M.A. Neifeld, “The speed of information in a ‘fast light’ optical medium,” Nature 425 , 695 (2003). 

