Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks

The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a simple time-dependent, Bloch-oscillating quantum walk enables th...

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Bibliographic Details
Published in:Physical review letters 2017-03, Vol.118 (13), p.130501-130501, Article 130501
Main Authors: Ramasesh, V V, Flurin, E, Rudner, M, Siddiqi, I, Yao, N Y
Format: Article
Language:English
Subjects:
Band structure of solids
Holes
Invariants
Qubits (quantum computing)
Strategy
Superconductivity
Time dependence
Topology
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Summary:The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a simple time-dependent, Bloch-oscillating quantum walk enables the direct measurement of topological invariants. We consider two classes of one-dimensional quantum walks and connect the global phase imprinted on the walker with its refocusing behavior. By disentangling the dynamical and geometric contributions to this phase, we describe a general strategy to measure the topological invariant in these quantum walks. As an example, we propose an experimental protocol in a circuit QED architecture where a superconducting transmon qubit plays the role of the coin, while the quantum walk takes place in the phase space of a cavity.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.118.130501