Measuring the atomic excitation time due to narrowband resonant photons that are transmitted

If a resonant photon traverses a medium and is transmitted on the far side, does it excite any atoms along the way? Previous work (PRX Quantum 3, 010314) provides evidence that it does. Since this work was limited to measurements using only broadband pulses of light, it cannot distinguish between recent theories that make strikingly different predictions in the case of excitation with narrowband pulses and media with low optical depth. In particular, the weak-value formalism suggests that this excitation time could be negative under such conditions. We present experimental progress to investigate this prediction and aim to fully elucidate the history of resonant photons that are ultimately transmitted through a cold cloud of 85Rb atoms.