Resonant scattering of a single atom with gain: A wave-function-diagrammatic approach

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