Erlangen 2018 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 15: Quantum Information (Concepts and Methods) II
Q 15.6: Vortrag
Montag, 5. März 2018, 15:30–15:45, K 1.019
Prime number decomposition using the Talbot effect — Karl Pelka1, •Jasmin Graf1, Thomas Mehringer1,2, and Joachim von Zanthier1,2 — 1Institut für Optik, Information und Photonik, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany — 2Erlangen Graduate School in Advanced Optical Technologies (SAOT), Universität Erlangen-Nürnberg, 91052 Erlangen, Germany
The Talbot effect is a near field diffraction effect describing the self imaging of a coherently illuminated transmission grating. Mathematically, this effect can be described by Gauss sums, which are connected to prime number decomposition. We present a novel algorithm for prime factorization which exploits the appearance of Gauss sums in the near field intensity distribution behind a single slit of the grating. We discuss the theoretical framework of this algorithm and report on an experimental implementation displaying an impressive agreement with the theoretical predictions.
We also investigate the regime of an incoherently illuminated grating where no first order interference signal is obtained. However, all relevant information can be regained by measuring the intensity correlations of second order. We explain how Gauss sums appear in the second order correlation function and how this signal can be used for prime number decomposition. As an outlook we present the experimental setup for measuring incoherent Talbot-like effects.