Factorization of Numbers with the Temporal Talbot Effect: Optical Implementation by a Sequence of Shaped Ultrashort Pulses

2007/09/30 by Damien Bigourd, Béatrice Chatel, B. Chatel +3 · 4 citations
Computer Science · Physics and Astronomy · #Laser-Matter Interactions and Applications #Orbital Angular Momentum in Optics #Quantum Information and Cryptography #physics.optics

paper · pdf · doi:10.1103/physrevlett.100.030202

published as Physical Review Letters 100, 03 (2008) 030202

arxiv created 2007/11/05 · openalex publication_date 2008/01/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Number-theoretic expressions obtained through analogy between prime factorization and optical interferometry
• Direct measurement of the Kirkwood-Rihaczek distribution for the spatial properties of a coherent light beam
• Quantum phase measurement and Gauss sum factorization of large integers in a superconducting circuit
• Quantum oscillations and wave packet revival in conical graphene structure

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