Phase advance of photons generated in stimulated emission relative to incident light

Kevin A. Fischer

Stimulated emission can be defined as the process when an incoming photon stimulates an additional quantum of energy from an atom into the same electromagnetic mode as the impinging photon. Hence, the two outgoing photons are identical. In a waveguide or free space, this intuition is typically found through Fermi's Golden rule, however, this does not properly account for the wave-like nature of the photons. Here, I present an exact solution to stimulated emission from a quantum two-level atom that properly accounts for the incoming and outgoing electromagnetic modes. This result is valid over a huge range of incident photon numbers. For a single incident photon, it shows how the photon must properly mode match the two-level system to cause stimulated emission. For a Fock state drive with large photon number, the exact solution shows how a two-level system Rabi oscillates with the traveling Fock mode as it passes by. I additionally use the same formalism to show that stimulated emission by a coherent pulse cannot be understood as an additional photon being emitted into the incident coherent state because the two-level system's state factorizes with the electromagnetic field's coherent state. Recent advances in superconducting circuits make them an ideal platform to test these predictions.

Masahiko HIROOKA

A. F. Harvey

Markus Pollnau

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.

Hyun Ho Choi, Hyung-Ju Kim, Jaewoo Noh +1 more

Andreas Reichegger, Jörg Evers

The temporal dynamics of stimulated emission is studied, with particular emphasis on stimulated emission induced by x-ray pulses interacting with nuclei. In typical nuclear forward scattering experiments, the short incident x-ray pulse is accompanied by a huge number of off-resonant background photons. This prompts the question of whether stimulated emission can be observed in the delayed nuclear scattering signal which is emitted after the incident pulse has passed. We find that the stimulated photons essentially overlap with the stimulating pulse. To overcome this problem, we identify the reduction of the delayed scattered light intensity as an alternative signature for the stimulated emission. We further study a phase-sensitive variant of stimulated emission in the low-excitation regime, which provides convenient control parameters to facilitate the detection. Finally, we analyze the possibility of observing stimulated emission in nuclei driven by free electron lasers or synchrotron radiation sources.