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.Received 9 March 2021Revised 23 August 2021Accepted 9 December 2021DOI:https://doi.org/10.1103/PRXQuantum.3.010314Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEffects of atomic coherence on light propagationEntanglement in quantum gasesLight-matter interactionQuantum opticsSpontaneous emissionPhysical SystemsAtomic ensembleTechniquesKerr effectWeak measurementsAtomic, Molecular & Optical
Highlights
When a resonant photon passes through a sample of atoms, the photon can either be absorbed (“lost”) or transmitted
It turns out that until now, there has been no measurement of how much time atoms spend in the excited state due to the passage of a resonant photon that is transmitted
The excitation time τe, which is a measure of the degree of atomic excitation induced by the signal pulse, has units of time, represents a duration, and provides an operational definition of the time atoms spend in the excited state
Summary
When a resonant photon passes through a sample of atoms, the photon can either be absorbed (“lost”) or transmitted. One could take the point of view that light is an electromagnetic field that polarizes atoms—irrespective of whether a given photon is transmitted or lost— creating a small excitation probability wherever it is present in the medium In this latter, “egalitarian,” picture, lost and transmitted photons both excite atoms but they still behave differently, because the former are, on average, scattered within the first optical decay length, while the latter have the opportunity to polarize the entire sample. “egalitarian,” picture, lost and transmitted photons both excite atoms but they still behave differently, because the former are, on average, scattered within the first optical decay length, while the latter have the opportunity to polarize the entire sample Does this mean that transmitted photons cause atoms to cumulatively spend more time in the excited state than do absorbed ones? Does this mean that transmitted photons cause atoms to cumulatively spend more time in the excited state than do absorbed ones? Questions such as these about the past behavior of a quantum particle, or about trajectories in
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