Quantum second harmonic generation in terms of elementary processes

We address the quantum dynamics of second harmonic generation with a perturbative approach. By inspecting the Taylor expansion of the unitary evolution, we identify the subsequent application of annihilation and creation operators as elementary processes and find out how the expansion of the second-harmonic photon-number probability distribution can be expressed in terms of the interplay of these processes. We show that overlaps between the output states of different elementary processes contribute to the expansion of the probability distribution and provide a diagrammatic technique to analytically retrieve terms of the distribution expansion at any order.

Automated summary

This paper addresses the quantum dynamics of second harmonic generation using a perturbative approach. By examining the Taylor expansion of the unitary evolution, the subsequent application of annihilation and creation operators is identified as elementary processes. The authors find out how the expansion of the second-harmonic photon-number probability distribution can be expressed in terms of the interplay of these processes. Overlaps between the output states of different elementary processes are shown to contribute to the expansion of the probability distribution, and a diagrammatic technique is provided to analytically retrieve terms of the distribution expansion at any order.