Darmstadt 2008 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 6: Quanteninformation (Atome und Ionen II)

Q 6.9: Talk

Monday, March 10, 2008, 18:30–18:45, 1B

Gauss sum factorization with cold atoms — •Michael Gilowski, Thijs Wendrich, Christian Schubert, Ernst M. Rasel, and Wolfgang Ertmer — Institut für Quantenoptik, Leibniz Universität Hannover

A factorization scheme taking advantage of the periodicity properties of Gauss sums has been proposed [1] and recently verified by two NMR-experiments [2] and one experiment based on short laser pulses [3]. In the present contribution we report the first implementation of a Gauss sum factorization based on matter-wave interferometry with cold rubidium atoms [4].

The implementation of the Gauss sums is performed by applying a sequence of light pulses which imprints on a two-level quantum system a sequence of well-defined phases. For appropriately chosen pulses the excitation probability takes the form of a Gauss sum. With this technique we factor the number N=263193. In contrast to the Shor algorithm our method in the present form is based on classical atomic ensembles and does not take benefit of the parallel computing of quantum information. The experimental realization as well as the results of the factorization experiment will be presented. This work is supported by SFB 407 and the FINAQS cooperation of the European Union.

[1] Clauser, et al. Phys. Rev. A 53, 4587 (1996) and Harter, et al. Phys. Rev. A 64, 012312 (2001) [2] Mehring, et al. Phys. Rev. Lett. 98, 120502 (2007) and Mahesh, et al. Phys. Rev. A 75, 062303 (2007). [3] Bigourd, et al. Phys. Rev. Lett. in press. [4] Gilowski, et al. Phys. Rev. Lett. in press.