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How much time does a photon spend as an atomic excitation before being transmitted through a cloud of atoms?

The propagation of a beam of light through a cloud of two-level atoms is among the most ubiquitous phenomena in atomic, molecular, and optical physics. Understanding the coherent effects of light on atoms, and the slowing, refraction, absorption, and scattering of light by atoms underlies the entire field. It has been pivotal in the conceptual development of Quantum Optics from Einstein’s early analysis of wave-particle duality up through today’s studies of cavity QED, nonclassical states...

Publication Date: September 22, 2025

Authors: Kyle Thompson, Kehui Li, Daniela Angulo, Vida-Michelle Nixon, Josiah Sinclair, Amal Vijayalekshmi Sivakumar, Howard M Wiseman, Aephraim M Steinberg

Abstract:

When a single photon propagates through a cloud of two-level atoms, part of its energy is temporarily stored as a collective atomic excitation. This raises a fundamental question: is it possible to meaningfully quantify how long the photon spends in the form of an atomic excitation? If so, does this duration depend on whether the photon is ultimately transmitted through the cloud or scattered by the atoms? These questions motivated recent experimental work by some of us [Sinclair et al., PRX Quantum 3, 010314 (2022)], but until now there has been no theoretical prediction for these conditional durations. We answer these questions by extending the concept of a dwell time from quantum tunneling to light–matter interactions, introducing an experimentally measurable “atomic excitation time.” Using the weak-value formalism combined with quantum trajectory theory, we derive analytical expressions for this time conditioned on the photon being transmitted through the cloud or scattered into a side mode. We show that, for transmitted photons, this time is equal to the (spectrally averaged) group delay, even in regimes where the group delay is negative. For scattered photons, the time is given by the sum of an ensemble-averaged group delay and an always-positive Wigner time delay, well known in elastic scattering theory. Finally, we present a toy model that explains how such negative dwell times can arise as a result of quantum interference. This work provides new insight into the complex and surprising histories of photons traveling through absorptive media.

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