Field operator transformations in Quantum Optics using a novel graphical method with applications to beam splitters and interferometers

TL;DR

This paper introduces a new graphical method for efficiently computing field operator transformations in complex linear lossless optical devices in Quantum Optics, with applications to beam splitters and interferometers.

Contribution

The paper presents a novel graphical approach that simplifies and accelerates the calculation of field operator transformations in quantum optical systems.

Findings

The method effectively computes transformations for beam splitters and interferometers.

It handles both monochromatic and non-monochromatic light cases.

The approach scales well with increased optical setup complexity.

Abstract

In this paper we describe a novel, graphical method, allowing the fast computation of field operator transformations for linear lossless optical devices in Quantum Optics (QO). The advantage of this method grows with the complexity of the considered optical setup. As case studies we examine the field operator transformations for the beam splitter (BS), the Mach-Zehnder interferometer (MZI) and the double MZI. We consider the simple case with monochromatic input light, as well as extensions to the non-monochromatic case.