Measuring topological invariants in disordered discrete-time quantum walks

Sonja Barkhofen, Thomas Nitsche, Fabian Elster, Lennart Lorz, A. Gábris, Igor Jex, Christine Silberhorn

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

Quantum walks constitute a versatile platform for simulating transport phenomena on discrete graphs including topological material properties while providing a high control over the relevant parameters at the same time. To experimentally access and directly measure the topological invariants of quantum walks, we implement the scattering scheme proposed by Tarasinski et al. [Phys. Rev. A 89, 042327 (2014)PLRAAN1050-294710.1103/PhysRevA.89.042327] in a photonic time multiplexed quantum walk experiment. The tunable coin operation provides opportunity to reach distinct topological phases, and accordingly to observe the corresponding topological phase transitions. The ability to read-out the position and the coin state distribution, complemented by explicit interferometric sign measurements, allowed the reconstruction of the scattered reflection amplitudes and thus the computation of the associated bulk topological invariants. As predicted, we also find localized states at the edges between two bulks belonging to different topological phases. In order to analyze the impact of disorder, we have measured invariants of two different types of disordered samples in large ensemble measurements, demonstrating their constancy in one disorder regime and a continuous transition with increasing disorder strength for the second disorder sample.

Original languageEnglish
Article number033846
JournalPhysical Review A
Volume96
Issue number3
DOIs
Publication statusPublished - Sep 27 2017

Fingerprint

disorders
platforms
photonics
scattering

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Barkhofen, S., Nitsche, T., Elster, F., Lorz, L., Gábris, A., Jex, I., & Silberhorn, C. (2017). Measuring topological invariants in disordered discrete-time quantum walks. Physical Review A, 96(3), [033846]. https://doi.org/10.1103/PhysRevA.96.033846

Measuring topological invariants in disordered discrete-time quantum walks. / Barkhofen, Sonja; Nitsche, Thomas; Elster, Fabian; Lorz, Lennart; Gábris, A.; Jex, Igor; Silberhorn, Christine.

In: Physical Review A, Vol. 96, No. 3, 033846, 27.09.2017.

Research output: Contribution to journalArticle

Barkhofen, S, Nitsche, T, Elster, F, Lorz, L, Gábris, A, Jex, I & Silberhorn, C 2017, 'Measuring topological invariants in disordered discrete-time quantum walks', Physical Review A, vol. 96, no. 3, 033846. https://doi.org/10.1103/PhysRevA.96.033846
Barkhofen, Sonja ; Nitsche, Thomas ; Elster, Fabian ; Lorz, Lennart ; Gábris, A. ; Jex, Igor ; Silberhorn, Christine. / Measuring topological invariants in disordered discrete-time quantum walks. In: Physical Review A. 2017 ; Vol. 96, No. 3.
@article{a6f1f26ebe374cf5b6fc57b03a99cab9,
title = "Measuring topological invariants in disordered discrete-time quantum walks",
abstract = "Quantum walks constitute a versatile platform for simulating transport phenomena on discrete graphs including topological material properties while providing a high control over the relevant parameters at the same time. To experimentally access and directly measure the topological invariants of quantum walks, we implement the scattering scheme proposed by Tarasinski et al. [Phys. Rev. A 89, 042327 (2014)PLRAAN1050-294710.1103/PhysRevA.89.042327] in a photonic time multiplexed quantum walk experiment. The tunable coin operation provides opportunity to reach distinct topological phases, and accordingly to observe the corresponding topological phase transitions. The ability to read-out the position and the coin state distribution, complemented by explicit interferometric sign measurements, allowed the reconstruction of the scattered reflection amplitudes and thus the computation of the associated bulk topological invariants. As predicted, we also find localized states at the edges between two bulks belonging to different topological phases. In order to analyze the impact of disorder, we have measured invariants of two different types of disordered samples in large ensemble measurements, demonstrating their constancy in one disorder regime and a continuous transition with increasing disorder strength for the second disorder sample.",
author = "Sonja Barkhofen and Thomas Nitsche and Fabian Elster and Lennart Lorz and A. G{\'a}bris and Igor Jex and Christine Silberhorn",
year = "2017",
month = "9",
day = "27",
doi = "10.1103/PhysRevA.96.033846",
language = "English",
volume = "96",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "3",

}

TY - JOUR

T1 - Measuring topological invariants in disordered discrete-time quantum walks

AU - Barkhofen, Sonja

AU - Nitsche, Thomas

AU - Elster, Fabian

AU - Lorz, Lennart

AU - Gábris, A.

AU - Jex, Igor

AU - Silberhorn, Christine

PY - 2017/9/27

Y1 - 2017/9/27

N2 - Quantum walks constitute a versatile platform for simulating transport phenomena on discrete graphs including topological material properties while providing a high control over the relevant parameters at the same time. To experimentally access and directly measure the topological invariants of quantum walks, we implement the scattering scheme proposed by Tarasinski et al. [Phys. Rev. A 89, 042327 (2014)PLRAAN1050-294710.1103/PhysRevA.89.042327] in a photonic time multiplexed quantum walk experiment. The tunable coin operation provides opportunity to reach distinct topological phases, and accordingly to observe the corresponding topological phase transitions. The ability to read-out the position and the coin state distribution, complemented by explicit interferometric sign measurements, allowed the reconstruction of the scattered reflection amplitudes and thus the computation of the associated bulk topological invariants. As predicted, we also find localized states at the edges between two bulks belonging to different topological phases. In order to analyze the impact of disorder, we have measured invariants of two different types of disordered samples in large ensemble measurements, demonstrating their constancy in one disorder regime and a continuous transition with increasing disorder strength for the second disorder sample.

AB - Quantum walks constitute a versatile platform for simulating transport phenomena on discrete graphs including topological material properties while providing a high control over the relevant parameters at the same time. To experimentally access and directly measure the topological invariants of quantum walks, we implement the scattering scheme proposed by Tarasinski et al. [Phys. Rev. A 89, 042327 (2014)PLRAAN1050-294710.1103/PhysRevA.89.042327] in a photonic time multiplexed quantum walk experiment. The tunable coin operation provides opportunity to reach distinct topological phases, and accordingly to observe the corresponding topological phase transitions. The ability to read-out the position and the coin state distribution, complemented by explicit interferometric sign measurements, allowed the reconstruction of the scattered reflection amplitudes and thus the computation of the associated bulk topological invariants. As predicted, we also find localized states at the edges between two bulks belonging to different topological phases. In order to analyze the impact of disorder, we have measured invariants of two different types of disordered samples in large ensemble measurements, demonstrating their constancy in one disorder regime and a continuous transition with increasing disorder strength for the second disorder sample.

UR - http://www.scopus.com/inward/record.url?scp=85030321991&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030321991&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.96.033846

DO - 10.1103/PhysRevA.96.033846

M3 - Article

AN - SCOPUS:85030321991

VL - 96

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 3

M1 - 033846

ER -