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 L$_{A}$ L$_{D}$ = | − 6 + 36( ω 21 /γ ) 2 − 6( ω 21 /γ ) $^{4}$| 2 γT 0 [( ω 21 /γ ) 2 + 1][6( ω 21 /γ ) 2 − 2] , (3) 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). 14