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Detecting topological invariants of quantum walks via weak measurements and losses Asboth, Janos


Topological insulators have Hamiltonians with bulk topological invariants, which control the interesting processes at the surface of the system, but are hard to measure directly. We have found a way to measure the bulk topological invariant (winding number) of one-dimensional topological insulator Hamiltonians and quantum walks with chiral symmetry: it is given by the displacement of a single particle, observed via losses [1]. 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. In our repeated measurement scheme these losses occur at the end of every timestep. In the limit of rapidly repeated, vanishingly weak measurements, this corresponds to non-Hermitian Hamiltonians, such as the lossy Su-Schrieffer-Heeger model [2]. Contrary to intuition, the time needed to detect the winding number can be made shorter by decreasing the efficiency of the measurement. Our scheme has since been used to measure the bulk topological invariants of a discrete-time quantum walk on photons [3].

[1] T Rakovszky, JK Asboth, and A Alberti, Phys. Rev. B 95, 201407 (2017).
[2] MS Rudner and LS Levitov, Phys. Rev. Lett. 102, 065703 (2009).
[3] X Zhan et al, Phys. Rev. Lett. 119, 130501 (2017).

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