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

When a resonant photon traverses a sample of absorbing atoms, how much time do atoms spend in the excited state? Does the answer depend on whether the photon is ultimately absorbed or transmitted? In an experiment with ultra-cold Rubidium atoms, we simultaneously record whether atoms are excited by incident photons and whether those photons are transmitted. We measure the time spent by atoms in the excited state by using a separate laser to monitor the index of refraction of the sample and use direct detection to isolate the effect of single transmitted photons. We find that the average time atoms spend in the excited state due to one transmitted photon is not zero, but rather (77 +/- 16)% of the time the average incident photon causes them to spend in the excited state. We attribute this observation of "excitation without loss'' to coherent forward emission, which happens naturally when a broadband pulse propagates through an optically thick medium. These results unambiguously reveal the history of photons as they propagate through an absorbing medium and illustrate the power of utilizing post-selection to experimentally investigate the past of observed quantum systems.