# Freiburg 2019 – wissenschaftliches Programm

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# FM: Fall Meeting

## FM 63: Poster: Enabling Technologies: Quantum Materials, Quantum Dots, Quantum Wires, Point Contacts and Superconducting Systems

### FM 63.13: Poster

### Mittwoch, 25. September 2019, 16:30–18:30, Tents

Physical implementation of quantum walks in effective Dirac systems — •Vanessa Junk, Phillipp Reck, Cosimo Gorini, and Klaus Richter — Institut für Theoretische Physik, Universität Regensburg, Germany

Scientific interest in quantum walks (QW) [1] originally arose in the field of quantum computation since QWs can replace classical random walks and thus pose a powerful tool to speed up classical algorithms. In the last years however, QWs have become particularly promising to simulate different topological phases [2].

We will present how to physically implement such a QW in an effective Dirac system like graphene. Our proposal is based on the extension of the concept of the Quantum Time Mirror [3]. In the latter, a pulse coupling both branches of the Dirac cone is used to split an initial wave-packet into two parts moving in opposed directions. The amplitudes of the two parts can be adjusted via the pulse length. Hence, the pulse represents the ‘coin toss’ [4] in general QWs with the advantage of offering additional degrees of freedom. By periodically repeating the pulse, the initial wave-packet performs a QW. Since the walk is realized in a spatially continuous Dirac system instead of on a fixed graph, we can arbitrarily time the pulses and create a further variety in the resulting probability distribution of the wave-packet in space.

[1] Y. Aharonov, et al., Phys. Rev. A 48, 1687-1690 (1993)

[2] T. Kitagawa, Quantum Inf Process 11, 1107 (2012)

[3] P. Reck, et al., Phys. Rev. B 95, 165421 (2017)

[4] J. Kempe, Contemporary Physics 44, 307-327 (2003)