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 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.

© 2018 Optical Society of America

Improved discrete fractional Fourier transform

Soo-Chang Pei and Min-Hung Yeh
Opt. Lett. 22(14) 1047-1049 (1997)

Geometry and dynamics in the fractional discrete Fourier transform

Kurt Bernardo Wolf and Guillermo Krötzsch
J. Opt. Soc. Am. A 24(3) 651-658 (2007)

Multiphoton synthetic lattices in multiport waveguide arrays: synthetic atoms and Fock graphs

Konrad Tschernig, Roberto de J. León-Montiel, Armando Pérez-Leija, and Kurt Busch
Photon. Res. 8(7) 1161-1170 (2020)

Collision dynamics of a discrete soliton in uniform waveguide arrays

Anuj P. Lara and Samudra Roy
J. Opt. Soc. Am. B 40(3) 594-603 (2023)

Discrete fractional Fourier transform as a fast algorithm for evaluating the diffraction pattern of pulsed radiation

Magdy Tawfik Hanna, Amr Mohamed Shaarawi, Nabila Philip Attalla Seif, and Waleed Abd El Maguid Ahmed
J. Opt. Soc. Am. A 28(8) 1610-1619 (2011)