A single photon traveling through space follows a straight line unless it runs into something, behaving more or less like a billiard ball in Newtonian physics. Much of the optical behavior that we are used to seeing on a macroscopic scale, like reflection and refraction, is the result of scattering, in which light interacts with atoms or molecules, and may bounce off in some direction without gaining or losing energy.

Whereas we usually picture two ideal billiard balls bouncing off each other instantaneously, Wigner showed in 1955 that the scattering process takes some small amount of time. From a quantum mechanical point of view, we can think of the atom absorbing the photon and using its energy to excite an electron. A short time later, the electron relaxes and emits another photon, which continues on its way with no energy being lost in the process.

Since electrons can only be excited to particular energy levels, most colors of light are ignored by the atom. Only when the optical energy is close to one of the atom’s electron transition energies do we see so-called resonant scattering. In that case, the Wigner time delay is predicted to be on the order of 20-40 nanoseconds, or about the time it takes light to travel 6-12 meters. It should also depend on exactly how close we are to an electron transition energy.

The authors of this paper not only derive the expected time delay, but manage to measure it by looking at interactions of single photons with a single atom. They chose Rubidium⁸⁷, since it can be trapped by magnetic fields in a vacuum, and only has one electron on its outer shell, making the theory (relatively) easy. The Rubidium atom is held in place and irradiated with a very weak laser beam, which is turned on and off in “pulses,” so that each pulse duration is only about 60 nanoseconds. After the atom, a detector sees two light pulses. The first one consists of photons which pass through the atom undisturbed, and the second consists of any photons that were absorbed and re-emitted by the atom. Naturally, the experiment must be repeated thousands of times because of the tiny number of photons involved, and the experimenters must be careful that the atom doesn’t “heat up” and escape the magnetic trap. By looking at the statistics of the arrival times of the second batch of photons, the average time delay can be found.

The authors finds in this case that the time delay agrees well with theoretical predictions. Measuring the Wigner time delay for a single, simple atom allows us to model more complicated systems of densely packed atoms, where light might be scattered many times, and the energy levels of each atom might be affected by its local environment.

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