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Quantum Carpets: Factorization with Degeneracies

  • Sabine Wölk
  • Wolfgang P. Schleich
Chapter

Abstract

In this paper, we connect our approach of factoring numbers using the continuous truncated Gauss sum (Wölk et al., J. Mod. Optic, 2009) with the phenomenon of quantum carpets. In particular, we demonstrate that the degree of degeneracy of the ratio N translates into a crossing of the canals and ridges contained in the design of quantum carpets. In this way, quantum carpets represent an experimental implementation of our idea of factorization with degeneracies.

Keywords

Wave Packet Factorization Scheme Factor Number Gaussian Wave Packet Revival Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgment

We are grateful to M. Jakob, K.A.H. van Leuwwen, M. Štefańǎk, and M.S. Zubairy for many fruitful discussions on this topic. In this context, one of us (WPS) appreciates the inspiring discussions at the University of Vienna in the summer of 2009 with W. Case and M. Tomandl. This research was partially supported by the Max Planck Prize of WPS awarded by the Humboldt Foundation and the Max Planck Society. Moreover, WPS expresses his sincere thanks to the organizers L. Cohen and M.O. Scully of the Middleton Festival in Princeton 2007 for a most stimulating conference.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institut für QuantenphysikUniversität UlmUlmGermany

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