Hannover 2013 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 41: Quantum information: Concepts and methods III
Q 41.6: Vortrag
Mittwoch, 20. März 2013, 15:30–15:45, E 214
Quantum Walks with Nonorthogonal Position States — •Robert Matjeschk1, Andre Ahlbrecht1, Martin Enderlein2, Christopher Cedzich1, Albert H. Werner1, Michael Keyl3, Tobias Schaetz2, and Reinhard F. Werner1 — 1Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167 Hannover, Germany — 2Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Str. 3, 79104 Freiburg, Germany — 3ISI Foundation, Via Alassio 11/c, 10126 Torino - Italy
Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develop a general description of such a quantum walk and show how to map it into a standard one with orthogonal states, thereby making available all the tools developed for the latter. This enables a variety of experiments, which can be implemented with smaller step sizes and more steps. Tuning the non-orthogonality allows for an easy preparation of extended states such as momentum eigenstates, which travel at a well-defined speed with low dispersion. We introduce a method to adjust their velocity by momentum shifts, which allows to experimentally probe the dispersion relation, providing a benchmarking tool for the quantum walk, and to investigate intriguing effects such as the analog of Bloch oscillations.