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

Damien Bigourd (1, 2) , Béatrice Chatel (1) , Wolfgang P. Schleich (3) , Bertrand Girard (1)

1 Femto (LCAR)
2 LCAR - Laboratoire Collisions Agrégats Réactivité
3 Abteilung Quantenphysik

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.

Mots clés: Gauss sum; factorization; number theory; interferences

Domaines: Optique [physics.optics]

Damien Bigourd, Béatrice Chatel, Wolfgang P. Schleich, Bertrand Girard. Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses. Physical Review Letters, 2008, 100 (03), pp.030202. ⟨10.1103/PhysRevLett.100.030202⟩. ⟨hal-00171664v2⟩