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Photons walking the line

Banff International Research Station for Mathematical Innovation and Discovery

Light is a fascinating medium. It is interesting on its own but is equally well suited to be the tool for mimicking other physical systems. Recently considerable attention was given to processes called quantum walks. The quantum walk [1-2] is an excellent tool for modeling, simulating and testing a wide range of physical processes and effects. Quantum walks are defined as specific generalizations of classical (random) walks. The simplest model of a walk-the one dimensional discrete quantum walk (on a line)-is based on the combination of the dynamics of the internal degree of freedom defined by the coin operator and the conditioned shift in position space (step operator). The evolution of the walk is given by the repeated application of the resulting evolution operator. The coin as well as the step operator can suffer from imperfections and this leads to deviations from the ideal situation. The way how the ideal situation is alternated leads to additional interesting effects. We present results on theoretical and experimental studies of ideal and perturbed quantum walks [3-8] based on the all optical implementation of quantum walks. We point out the main results and future trends. <BR><BR> References <BR> [1] Y. Aharonov, L. Davidovich, N. Zagury, Phys. Rev. A 48, 1687 (1993). <BR> [2] D. A. Meyer, J. Stat. Phys. 85, 551 (1996). <BR> [3] A. Schreiber, K. N. Cassemiro, V. Potocek, A. Gabris, P.J. Mosley, E. Andersson, I. Jex, Ch. Silberhorn, Phys. Rev. Lett. 104, 050502 (2010). <BR> [4] A. Schreiber, K. N. Cassemiro, V. Potocek, A. Gábris, E, I. Jex, Ch. Silberhorn, Phys. Rev. Lett. 104, 050502 (2011). <BR> [5] A. Schreiber, A. Gábris, P. P. Rohde, K. Laiho, M. Štefanák, V. Potocek, C. Hamilton, I. Jex, Ch. Silberhorn,. Science 336, 55 (2012). <BR> [6] F. Elster, S. Barkhofen, T. Nitsche, J. Novotný, A. Gábris, I. Jex, Ch. Silberhorn, Sci. Rep. 5 (2015) 13495. <BR> [7] T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, Ch. Silberhorn, New J. Phys. 18 (2016) 063017. <BR> [8] T. Nitsche, S. Barkhofen, R. Kruse, L. Sansoni, M. Štefanák, A. Gábris, V. Potocek, T. Kiss, I. Jex, Ch. Silberhorn, Science Adv. 4, eaar6444 (2018).

Mathematics; Quantum theory; Mathematical physics

video/mp4

Author affiliation: Czech Technical University

2019-10-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/71975

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/