A graphical method in quantum optics

Abstract

In this paper we describe in detail a graphical method allowing the computation of field operator transformations in quantum optics(QO). Its applications include beam splitters(BS), Mach-Zehnder interferometers(MZI), optical resonators(Fabry–Perot etc) as well as non-linear crystals featuring the process of spontaneous parametric down-conversion (SPDC). Its main advantage compared to the traditional computation step-by-step method is its visual and intuitive approach, somehow similar to Feynman’s diagrammatic approach in Quantum Field Theory. It also seems adapted to computerbased implementations since calculations mainly consist on complex additions and multiplications, not matrix operations.