# Laboratoire Collisions Agrégats Réactivité - UMR5589

Université Paul Sabatier - Bat. 3R4 - 118 route de Narbonne 31062 Toulouse Cedex 09, France

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

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.

doi:10.1103/PhysRevLett.100.030202

Voir en ligne : Phys. Rev. Lett. 100, 030202 (2008)