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# Competition and interplay between topology and quasi-periodic disorder in Thouless pumping of ultracold atoms

## Abstract

Robustness against perturbations lies at the heart of topological phenomena. If, however, a perturbation such as disorder becomes dominant, it may cause a topological phase transition between topologically non-trivial and trivial phases. Here we experimentally reveal the competition and interplay between topology and quasi-periodic disorder in a Thouless pump realized with ultracold atoms in an optical lattice, by creating a quasi-periodic potential from weak to strong regimes in a controllable manner. We demonstrate a disorder-induced pumping in which the presence of quasi-periodic disorder can induce a non-trivial pump for a specific pumping sequence, whereas no pump is observed in the clean limit. Our highly controllable system, which can also straightforwardly incorporate interatomic interaction, could be a unique platform for studying various disorder-related effects in a wide range of topological quantum phenomena.

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• ### Two-dimensional Thouless pumping of light in photonic moiré lattices

Nature Communications Open Access 08 November 2022

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## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

## Code availability

The codes used for the numerical simulations within this paper are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank H. Aoki, Y. Hatsugai and K. Imura for valuable discussions and A. Sawada for experimental assistance. This work was supported by Grants-in-Aid for Scientific Research of the Japan Society for the Promotion of Science (JSPS) (grant nos. JP25220711, JP26247064, JP16H00990, JP16H01053, JP17H06138, JP18H05405, JP18H05228 and JP18K13480), the Impulsing Paradigm Change through Disruptive Technologies (ImPACT) programme, the CREST programme of the Japan Science and Technology Agency (grant no. JPMJCR1673) and the Quantum Leap Flagship Program of the Ministry of Education, Culture, Sports, Science and Technology (MEXT Q-LEAP) (grant no. JPMXS0118069021). Y.K. acknowledges the support of a Grant-in-Aid for JSPS Fellows (grant no. 17J00486). P.M. is supported by the JST (CREST grant. no. JPMJCR19T2), by the MEXT-supported Program for the Strategic Research Foundation at Private Universities Topological Science (grant no. S1511006) and by a JSPS Grant-in-Aid for Early-Career Scientists (grant no. 20K14375).

## Author information

Authors

### Contributions

S.N., N.T. and K.S. carried out experiments and the data analysis. Y.K. and P.M. carried out the theoretical calculation. Y.T. conducted the whole experiment. All the authors contributed to the writing of the manuscript.

### Corresponding author

Correspondence to Shuta Nakajima.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–10 and Discussion.

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Nakajima, S., Takei, N., Sakuma, K. et al. Competition and interplay between topology and quasi-periodic disorder in Thouless pumping of ultracold atoms. Nat. Phys. 17, 844–849 (2021). https://doi.org/10.1038/s41567-021-01229-9

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• DOI: https://doi.org/10.1038/s41567-021-01229-9

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