Berlin 2005 – scientific programme

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Q: Quantenoptik und Photonik

Q 21: Poster Quanteneffekte

Q 21.6: Poster

Monday, March 7, 2005, 11:00–12:30, Poster HU

Factorization of numbers using chirped pulses — •Wolfgang Merkel¹, Holger Mack¹, Eric Lutz¹, Gerhard Paulus², Bertrand Girard³, and Wolfgang P. Schleich¹ — ¹Abteilung für Quantenphysik, Universität Ulm, D-89069 Ulm — ²Texas A&M University, College Station — ³Universite Paul Sabatier, Toulouse

In this work we present a physical system that combines wavepacket dynamics and number theory. It has been shown that Gauss-sums, which involve quadratic phase factors, may be utilized to obtain the prime factor components of a given number N [1]. As the physical system we choose a two-photon transition which is driven by a chirped laser pulse [2]. In addition to a ground and an excited state the underlying level scheme contains a harmonic manifold of intermediate states. Quantum interference of multiple excitation paths is the key mechanism of this factorization scheme. We show how quadratic phase factors enter and present a recipe to encode the number N and reveal its prime components.
H. Mack, M. Bienert, F. Haug, M. Freyberger, and W.P. Schleich, phys. stat. sol. (b) 233, No. 3, 408-415 (2002)
B. Chatel, J. Degert, S. Stock, and B. Girard, Phys. Rev. A 68, 041402(R) (2003)