Exploring topological phases with quantum walks

Takuya Kitagawa, Mark S. Rudner, Erez Berg, and Eugene Demler
Phys. Rev. A 82, 033429 – Published 24 September 2010

Abstract

The quantum walk was originally proposed as a quantum-mechanical analog of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete-time quantum walks provide a versatile platform for studying topological phases, which are currently the subject of intense theoretical and experimental investigations. In particular, we demonstrate that recent experimental realizations of quantum walks with cold atoms, photons, and ions simulate a nontrivial one-dimensional topological phase. With simple modifications, the quantum walk can be engineered to realize all of the topological phases, which have been classified in one and two dimensions. We further discuss the existence of robust edge modes at phase boundaries, which provide experimental signatures for the nontrivial topological character of the system.

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  • Received 23 July 2010

DOI:https://doi.org/10.1103/PhysRevA.82.033429

©2010 American Physical Society

Authors & Affiliations

Takuya Kitagawa, Mark S. Rudner, Erez Berg, and Eugene Demler

  • Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

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Issue

Vol. 82, Iss. 3 — September 2010

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