TY - JOUR

T1 - Creating anomalous Floquet Chern insulators with magnetic quantum walks

AU - Sajid, Muhammad

AU - Asbóth, János K.

AU - Meschede, Dieter

AU - Werner, Reinhard F.

AU - Alberti, Andrea

N1 - Funding information: A.A. acknowledges insightful discussions with M. Fleischhauer and H. Kroha. We thank P. Arnault for early contributions to this work and numerous discussions. We also thank T. Groh's assistance for the estimate of the motional excitations while flashing the magnetic-field operator. We acknowledge financial support from the ERC grant DQSIM (Project No. 291401), and the collaborative research center OSCAR funded by the Deutsche Forschungsgemeinschaft (Project No. 277625399-TRR 185). M.S. also acknowledges support from the Deutscher Akademischer Austauschdienst. J.K.A. acknowledges support from the National Research, Development and Innovation Fund of Hungary within the Quantum Technology National Excellence Program (Project No. 2017-1.2.1-NKP-2017-00001), and FK 124723.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - We propose a realistic scheme to construct anomalous Floquet Chern topological insulators using spin-12 particles carrying out a discrete-time quantum walk in a two-dimensional lattice. By Floquet engineering the quantum-walk protocol, an Aharonov-Bohm geometric phase is imprinted onto closed-loop paths in the lattice, thus realizing an Abelian gauge field, the analog of a magnetic flux threading a two-dimensional electron gas. We show that in the strong-field regime, when the flux per plaquette is a sizable fraction of the flux quantum, magnetic quantum walks give rise to nearly flat energy bands featuring nonvanishing Chern numbers. Furthermore, we find that because of the nonperturbative nature of the periodic driving, a second topological number, the so-called RLBL invariant, is necessary to fully characterize the anomalous Floquet topological phases of magnetic quantum walks and to compute the number of topologically protected edge modes expected at the boundaries between different phases. In the second part of this paper, we discuss an implementation of this scheme using neutral atoms in two-dimensional spin-dependent optical lattices, which enables the generation of arbitrary magnetic-field landscapes, including those with sharp boundaries. The robust atom transport, which is observed along boundaries separating regions of different field strength, reveals the topological character of the Floquet Chern bands.

AB - We propose a realistic scheme to construct anomalous Floquet Chern topological insulators using spin-12 particles carrying out a discrete-time quantum walk in a two-dimensional lattice. By Floquet engineering the quantum-walk protocol, an Aharonov-Bohm geometric phase is imprinted onto closed-loop paths in the lattice, thus realizing an Abelian gauge field, the analog of a magnetic flux threading a two-dimensional electron gas. We show that in the strong-field regime, when the flux per plaquette is a sizable fraction of the flux quantum, magnetic quantum walks give rise to nearly flat energy bands featuring nonvanishing Chern numbers. Furthermore, we find that because of the nonperturbative nature of the periodic driving, a second topological number, the so-called RLBL invariant, is necessary to fully characterize the anomalous Floquet topological phases of magnetic quantum walks and to compute the number of topologically protected edge modes expected at the boundaries between different phases. In the second part of this paper, we discuss an implementation of this scheme using neutral atoms in two-dimensional spin-dependent optical lattices, which enables the generation of arbitrary magnetic-field landscapes, including those with sharp boundaries. The robust atom transport, which is observed along boundaries separating regions of different field strength, reveals the topological character of the Floquet Chern bands.

UR - http://www.scopus.com/inward/record.url?scp=85068610672&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1808.08923

DO - 10.48550/arXiv.1808.08923

M3 - Article

AN - SCOPUS:85068610672

VL - 99

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 21

M1 - 214303

ER -