Topological Transition in a Non-Hermitian Quantum Walk
Author(s)Levitov, Leonid; Rudner, Mark Spencer
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We analyze a quantum walk on a bipartite one-dimensional lattice, in which the particle can decay whenever it visits one of the two sublattices. The corresponding non-Hermitian tight-binding problem with a complex potential for the decaying sites exhibits two different phases, distinguished by a winding number defined in terms of the Bloch eigenstates in the Brillouin zone. We find that the mean displacement of a particle initially localized on one of the nondecaying sites can be expressed in terms of the winding number, and is therefore quantized as an integer, changing from zero to one at the critical point. We show that the topological transition is relevant for a variety of experimental settings. The quantized behavior can be used to distinguish coherent from incoherent dynamics.
DepartmentMassachusetts Institute of Technology. Department of Physics; Massachusetts Institute of Technology. Research Laboratory of Electronics
Physical Review Letters
American Physical Society
Rudner, M. S., and L. S. Levitov. “Topological Transition in a Non-Hermitian Quantum Walk.” Physical Review Letters 102.6 (2009): 065703. (C) 2010 The American Physical Society.
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