How much time does a photon spend as an atomic excitation before being transmitted?

TL;DR

This paper investigates the time photons spend as atomic excitations in a cloud of two-level atoms, revealing that transmitted photons' time correlates with group delay and scattered photons' time includes Wigner delay, challenging prior intuition.

Contribution

It introduces a weak-value formalism approach to accurately determine the time photons spend as atomic excitations, showing that transmitted photons can have positive or negative delays.

Findings

Transmitted photons' atomic excitation time equals the group delay.

Scattered photons' time includes both group delay and Wigner time delay.

The study refutes the simplistic view that transmitted photons spend zero time as excitations.

Abstract

When a single photon traverses a cloud of 2-level atoms, the average time it spends as an atomic excitation -- as measured by weakly probing the atoms -- can be shown to be the spontaneous lifetime of the atoms multiplied by the probability of the photon being scattered into a side mode. A tempting inference from this is that an average scattered photon spends one spontaneous lifetime as an atomic excitation, while photons that are transmitted spend zero time as atomic excitations. However, recent experimental work by some of us [PRX Quantum 3, 010314 (2022)] refutes this intuition. We examine this problem using the weak-value formalism and show that the time a transmitted photon spends as an atomic excitation is equal to the group delay, which can take on positive or negative values. We also determine the corresponding time for scattered photons and find that it is equal to the time delay of the scattered photon pulse, which consists of a group delay and a time delay associated with elastic scattering, known as the Wigner time delay. This work provides new insight into the complex and surprising histories of photons travelling through absorptive media.