Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties. In particular, it has been employed to study topological phenomena in a variety of different platforms. In driven systems, the topological properties of the quasienergy bands can often be determined by standard topological invariants, such as Chern numbers, which are commonly used in static systems. However, due to the periodic nature of the quasienergy spectrum, this topological description is incomplete and new invariants are required to fully capture the topological properties of these driven settings. Most prominently, there are two-dimensional anomalous Floquet systems that exhibit robust chiral edge modes, despite all Chern numbers being equal to zero. Here we realize such a system with bosonic atoms in a periodically driven honeycomb lattice and infer the complete set of topological invariants from energy gap measurements and local Hall deflections.
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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
The code that supports the plots within this paper are available from the corresponding author upon reasonable request.
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We thank J. Bellissard, E. Berg, J. Dalibard, E. Demler and N. Lindner for inspiring discussions. The research in Munich and Dresden was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via Research Unit FOR 2414 under project number 277974659. The work in Munich was further supported under Germany’s Excellence Strategy – EXC-2111 – 39081486. F.N.Ü. further acknowledges support from EPSRC grant number EP/P009565/1. The work in Belgium was supported by the ERC Starting Grant TopoCold, and the Fonds De La Recherche Scientifique (FRS-FNRS, Belgium).
The authors declare no competing interests.
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This Supplementary Information includes a presentation of the relevant calibration measurements and additional datasets, a detailed description of the theoretical model, a calculation of the edge states using a tight-binding model and a discussion of the theoretical connection between the topological charge and the Berry curvature.
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Wintersperger, K., Braun, C., Ünal, F.N. et al. Realization of an anomalous Floquet topological system with ultracold atoms. Nat. Phys. 16, 1058–1063 (2020). https://doi.org/10.1038/s41567-020-0949-y
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