Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses

TL;DR

This paper presents an optical analogue computer that uses shaped ultrashort laser pulses and the temporal Talbot effect to factor numbers by encoding them into Gauss sums through classical light interference.

Contribution

It introduces a novel optical implementation for number factorization using ultrashort pulses and the temporal Talbot effect, bridging laser physics and number theory.

Findings

Successfully demonstrated number factoring with an optical device

Utilized classical light interference to encode Gauss sums

Achieved potential for rapid, parallel number factorization

Abstract

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number.