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Detecting topological invariants in chiral symmetric insulators via losses

Tibor Rakovszky, János K. Asbóth, and Andrea Alberti
Phys. Rev. B 95, 201407(R) – Published 9 May 2017
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Abstract

We show that the bulk winding number characterizing one-dimensional topological insulators with chiral symmetry can be detected from the displacement of a single particle, observed via losses. Losses represent the effect of repeated weak measurements on one sublattice only, which interrupt the dynamics periodically. When these do not detect the particle, they realize negative measurements. Our repeated measurement scheme covers both time-independent and periodically driven (Floquet) topological insulators, with or without spatial disorder. In the limit of rapidly repeated, vanishingly weak measurements, our scheme describes non-Hermitian Hamiltonians, as the lossy Su-Schrieffer-Heeger model of Rudner and Levitov, [Phys. Rev. Lett. 102, 065703 (2009)]. We find, contrary to intuition, that the time needed to detect the winding number can be made shorter by decreasing the efficiency of the measurement. We illustrate our results on a discrete-time quantum walk, and propose ways of testing them experimentally.

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  • Received 14 December 2016

DOI:https://doi.org/10.1103/PhysRevB.95.201407

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Tibor Rakovszky1,2, János K. Asbóth3, and Andrea Alberti4

  • 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
  • 2Technische Universität München, D-85747 Garching, Germany
  • 3Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
  • 4Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, D-53115 Bonn, Germany

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Issue

Vol. 95, Iss. 20 — 15 May 2017

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