Factorization of numbers with Gauss sums: II. Suggestions for implementation with chirped laser pulses

Abstract

We propose three implementations of the Gauss sum factorization schemes discussed in part I of this series (Wölk et al 2011 New J. Phys. 13 103007): (i) A two-photon transition in a multi-level ladder system induced by a chirped laser pulse, (ii) A chirped one-photon transition in a two-level atom with a periodically modulated excited state and (iii) A linearly chirped onephoton transition driven by a sequence of ultrashort pulses. For each of these quantum systems, we show that the excitation probability amplitude is given by an appropriate Gauss sum. We provide rules on how to encode the number N to be factored in our system and how to identify the factors of N in the fluorescence signal of the excited state. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.