Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks

V. V. Ramasesh; E. Flurin; Mark Spencer Rudner; I. Siddiqi; N. Y. Yao

doi:10.1103/physrevlett.118.130501

Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks

V. V. Ramasesh^*, E. Flurin, Mark Spencer Rudner, I. Siddiqi, N. Y. Yao

^*Corresponding author for this work

Condensed Matter Physics

45 Citations (Scopus)

Abstract

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.

Original language	English
Article number	130501
Journal	Physical Review Letters
Volume	118
Issue number	13
Number of pages	6
ISSN	0031-9007
DOIs	https://doi.org/10.1103/physrevlett.118.130501
Publication status	Published - 2017

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PhysRevLett.118.130501Final published version, 771 KB

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title = "Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks",

abstract = "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.",

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AU - Yao, N. Y.

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N2 - 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.

AB - 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.

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JO - Physical Review Letters

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Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks

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