CHIRPED PULSES, GAUSS SUMS AND THE FACTORIZATION OF NUMBERS
Wolfgang Merkel, Oliver Crasser, Florian Haug, Eric A. Lutz, Holger Mack, Matthias Freyberger, Wolfgang P. Schleich, Ilya Sh. Averbukh, Marc Bienert, B. Girard, Helmut Maier, G. G. Paulus · International Journal of Modern Physics B · 2006
We present two physical systems which make Gauß sums experimentally accessible. The probability amplitude for a two-photon transition in an appropriate ladder system driven by a chirped laser pulse is determined by a Gauß sum. The autocorrelation function of a quantum rotor is also of the form of a Gauß sum. These examples suggest rules for determining prime factor components on the basis of the properties of Gauß sums. Moreover, we show how Gauß sums are related to the Riemann Zeta function.