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When a resonant photon traverses a sample of absorbing atoms, how much timedo atoms spend in the excited state? Does the answer depend on whether thephoton is ultimately absorbed or transmitted? In particular, if it is$\textit{not}$ absorbed, does it cause atoms to spend any time in the excitedstate, and if so, how much? In an experiment with ultra-cold Rubidium atoms, wesimultaneously record whether atoms are excited by incident ("signal") photonsand whether those photons are transmitted. We measure the time spent by atomsin the excited state by using a separate, off-resonant "probe" laser to monitorthe index of refraction of the sample - that is, we measure the nonlinear phaseshift written by a signal pulse on this probe beam - and use direct detectionto isolate the effect of single transmitted photons. For short pulses (10 ns,to be compared to the 26 ns atomic lifetime) and an optically thick medium(peak OD = 4, leading to 60% absorption given our broad bandwidth), we findthat the average time atoms spend in the excited state due to one transmittedphoton is not zero, but rather (77 $\pm$ 16)% of the time the average incidentphoton causes them to spend in the excited state. We attribute this observationof "excitation without loss" to coherent forward emission, which can arise whenthe instantaneous Rabi frequency (pulse envelope) picks up a phase flip - thishappens naturally when a broadband pulse propagates through an optically thickmedium with frequency-dependent absorption [1]. These results unambiguouslyreveal the complex history of photons as they propagate through an absorbingmedium and illustrate the power of utilizing post-selection to experimentallyinvestigate the past behaviour of observed quantum systems.

Measuring the time atoms spend in the excited state due to a photon they don't absorb