Measuring the time transmitted photons spend as atomic excitations

When a pulse of light propagates through a material, it incurs a temporal delay known as the group delay. Is it possible to attribute this temporal delay to the light spending time in the atoms as atomic excitations? Particularly since the group delay becomes negative on resonance and the attribution appears to break down. We experimentally explore this question by probing the duration of atomic excitation in a cloud of cold 85Rb atoms, caused by a propagating resonant photon which is transmitted through the cloud. In particular, we probe the excitations using a technique previously developed by our group, involving a weak cross-Kerr nonlinearity between the resonant photon and a continuous-wave probe. We test the dependence on both pulse bandwidth and optical depth of the medium, and found excitation times as negative as (-1.14 ± 0.22)τ₀, and as positive as (0.54 ± 0.28)τ₀ (τ₀ being the atomic excitation time caused by an average incident photon, regardless of the photon's fate). Our results suggest that negative time values, such as the group delay near resonance, have more physical significance than has generally been appreciated.