When off-resonant light passes through a material, it travels slower than it would in vacuum. This delay can be explained using the uncertainty principle: even when atoms are driven by light with a large detuning, δ, they can still be excited briefly, for a time on the order of 1/δ. This extra time spent as a non-propagating excitation is associated with the group delay. While this connection between group delay and the time a photon spends as an atomic excitation seems reasonable, it becomes problematic near atomic resonance, where the group delay turns negative.
To investigate this, I used the cross-Kerr effect to measure the degree of atomic excitation caused by a resonant transmitted photon, by observing the phase shift on a separate, weak, off-resonant beam. Across various pulse durations and optical depths, the results align with the recent theoretical prediction that the average atomic excitation time caused by a transmitted photon (measured via the time integral of the observed phase shift) equals the group delay. My findings confirm that the group delay is a physically meaningful quantity, not only indicating the position of the transmitted pulse but also accurately describing the magnitude—and sign—of the effect transmitted photons have on systems they interact with.