Exact calculation of stimulated emission driven by pulsed light

TL;DR

This paper provides an exact quantum mechanical solution for stimulated emission driven by pulsed light, accounting for wave-like photon properties and mode matching, with implications for superconducting circuit experiments.

Contribution

It introduces a precise solution for stimulated emission from a two-level atom that includes wave effects and mode matching, extending beyond traditional approximations.

Findings

Exact solution valid over a wide range of photon numbers

Mode matching is essential for stimulated emission with single photons

Stimulated emission by coherent pulses cannot be viewed as simple photon addition

Abstract

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.