Are absorption and spontaneous or stimulated emission inverse processes? The answer is subtle!

It is generally believed that absorption and stimulated emission are inverse processes, as both are driven by an external field, their strength is quantified by the same Einstein B coefficient, and they occur with a defined phase, opposite to each other, namely in phase and in anti-phase with the driving field, whereas spontaneous emission is a different process that occurs with an arbitrary phase with respect to a potential incident field. Recently, the phase relation in absorption and emission was shown to differ from this believe. Here it is verified via the amplitude–phase diagram and via the interference of sine waves that, precisely speaking, only the absorption process, in which a number φ + 1 of incident photons is decreased by one photon, and the emission process, in which a number φ of incident photons is increased by one photon, are truly inverse processes also in their phase. Particularly, this implies that absorption of a single incident photon and spontaneous emission of a photon into an empty mode are inverse processes in the amplitude–phase diagram.