Multiphoton Discrete Fractional Fourier Dynamics in Waveguide Beam Splitters

TL;DR

This paper reveals that multiphoton states in waveguide beam splitters behave like discrete fractional Fourier systems, leading to a generalized suppression law and enabling multiphoton quantum random walks with potential for high-dimensional quantum applications.

Contribution

It introduces a novel multiphoton suppression law based on discrete fractional Fourier transform properties and explores multiphoton quantum random walks in waveguide beam splitters.

Findings

Derived a multiphoton suppression law for 50/50 beam splitters.

Showed that multiphoton states evolve as coupled systems akin to fractional Fourier systems.

Proposed the use of waveguide beam splitters for high-dimensional multiphoton quantum walks.

Abstract

We demonstrate that when a waveguide beam splitter (BS) is excited by N indistinguishable photons, the arising multiphoton states evolve in a way as if they were coupled to each other with coupling strengths that are identical to the ones exhibited by a discrete fractional Fourier system. Based on the properties of the discrete fractional Fourier transform, we then derive a multiphoton suppression law for 50/50 BSs, thereby generalizing the Hong-Ou-Mandel effect. Furthermore, we examine the possibility of performing simultaneous multiphoton quantum random walks by using a single waveguide BS in combination with photon number resolving detectors. We anticipate that the multiphoton lattice-like structures unveiled in this work will be useful to identify new effects and applications of high-dimensional multiphoton states.