a GLYPH<RParen1> 8 10 12 14 0 0.2 0.4 0.6 t GLYPH<LParen1> ps GLYPH<RParen1> cross GLYPH<Minus> correlation b GLYPH<RParen1> 0 2 4 6 0 0.2 0.4 0.6 0.8 t GLYPH<LParen1> ps GLYPH<RParen1> cross GLYPH<Minus> correlation Fig. 3. (Color online) Comparison of experimental (solid line) and theoretically predicted (dashed line) results for a a) 650-fs-long pulse centered at λ$_{c}$ and a vapor temperature of 326 ◦ C and b) 250-fs-long pulse centered at 787.5 nm and a vapor temperature of 263 ◦ C. us to easily tune the group delay over almost 10 ps in a 7 cm cell. Knowing the full susceptibility of the vapor gives us complete knowledge of the vapor’s effective transfer function H ( ω ) and allows us to quantify the pulse distortion. While the distortion tolerances for a system can be highly specific to the intended application, we take two different approaches to place our work in context with other studies. First, we calculate the deviation of the Rubidium vapor’s transfer function from an ideal one for a given bandwidth of the incident pulse. The ideal transfer function, which induces no distortions, is defined as H$_{ideal}$ ( ω ) = H 0 exp ( iωt$_{p}$ ), where H 0 is a constant amplitude and t$_{p}$ is the total propagation time of the pulse. Using the concept of amplitude and phase distortion ( D$_{a}$ and D$_{p}$ , respectively) defined in Ref. [24], we find that phase distortion is the limiting quantity for realizing low-distortion delays over large bandwidths ( D$_{a}$ < 10 − 3 for the regime studied in this paper). We note that this measure of distortion is particularly relevant to our system because we use pulses with spectra that are well-approximated by a rectangular function. By defining a maximum-allowed distortion D $^{max}$, we calculate the largest achievable fractional delay for a given spectral bandwidth subject to the constraint that D$_{a}$, D$_{p}$ < D max (see Fig. 5). Thus, we find that one can realize f$_{D}$ > 1 over a bandwidth of several nanometers while 9