### Description

When a single photon traverses a cloud of 2-level atoms on resonance, how much time does it spend as an atomic excitation, as measured by weakly probing the atoms? It turns out that the answer, on average, is simply the spontaneous lifetime, multiplied by the probability of the photon being scattered into a side mode. It is tempting to infer from this that photons that are scattered spend, on average, one spontaneous lifetime as an atomic excitation, and photons that are transmitted through the cloud spend no time at all as an atomic excitation. Our recent experimental work [PRX Quantum 3, 010314] shows that this inference is incorrect, and that transmitted photons do spend time as atomic excitations. However, a complete theoretical treatment of the open-system dynamics for such a system has never, to our knowledge, been carried out. We examine this problem using the weak-value formalism, and find that the time that a transmitted photon spends as an atomic excitation is equal to the group delay experienced by the photon. Surprisingly, this equivalence remains true even for resonant, narrowband photons, for which the group delay is negative. We also determine the corresponding time for scattered photons, which turns out to be related to the "Wigner time" associated with elastic scattering. This work provides insight into the complex histories of photons travelling through absorptive media.

Presenter name | Kyle Thompson |
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How will you attend ICAP-27? | I am planning on in-person attendance |