Measuring the Time Atoms Spend in the Excited State Due to a Photon They Do Not Absorb

Abstract

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 particular, if it is not absorbed, does it cause atoms to spend any time in the excited state and if so, how much? To answer these questions, we perform an experiment with ultracold rubidium atoms in which we simultaneously record whether atoms are excited by incident (“signal”) photons and whether those photons are transmitted. We measure the time spent by atoms in the excited state by using a separate off-resonant “probe” laser to monitor the index of refraction of the sample—that is, we measure the nonlinear phase shift written by a signal pulse on this probe beam—and use direct detection to 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 optical depth equals 4, leading to 60% absorption given our broad bandwidth), 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 can arise when the instantaneous Rabi frequency (pulse envelope) picks up a 180^{∘} phase flip—this happens naturally when a broadband pulse propagates through an optically thick medium with frequency-dependent absorption. These results unambiguously reveal for the first time the complex history of photons as they propagate through an absorbing medium and illustrate the power of utilizing postselection to experimentally investigate the past behavior of observed quantum systems.