Resonant scattering of a single atom with gain: a wavefunction-diagrammatic approach

TL;DR

This paper develops a wavefunction-diagrammatic approach to analyze the optical response of a pumped three-level atom, revealing how gain, losses, and scattering are affected by incoherent pumping and identifying conditions for extinction vanishing.

Contribution

It introduces a novel wavefunction and diagrammatic method to characterize atomic scattering with gain, accounting for incoherent effects while reducing the system to an effective two-level model.

Findings

Pump reduces nonradiative losses and enhances stimulated emission.

Extinction vanishes at a specific pump rate related to natural decay.

Gain and losses balance at high pump, leading to zero extinction.

Abstract

We characterize the optical response of a three-level atom subjected to an incoherent pump and continuously illuminated with a weak, quasi-resonant probe field. To this end, we apply a wavefunction approach based on QED Hamiltonian perturbation theory which allows for a reduction of the atomic dynamics to that of an effective two-level atom, and for an implementation of the incoherent effects that respects unitarity. Using a diagrammatic representation, we identify and classify all the radiative processes. This allows us to compute the scattered power, the spontaneous emission, and the stimulated emission, as well as the total cross sections of extinction, absorption and scattering. We find that, beside a general enhancement of the linewidth and an attenuation of the spectral amplitudes, the pump reduces the nonradiative losses and provides gains in the form of stimulated emission and incoherent radiation. For sufficiently strong pump, gains and losses compensate, resulting in the vanishing of extinction. In particular, for negligible nonradiative losses, extinction vanishes for a pumping rate of $(1+\sqrt{5})/2$ times that of the natural decay.