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# Floquet approach to ℤ2 lattice gauge theories with ultracold atoms in optical lattices

## Abstract

Quantum simulation has the potential to investigate gauge theories in strongly interacting regimes, which are currently inaccessible through conventional numerical techniques. Here, we take a first step in this direction by implementing a Floquet-based method for studying $${\Bbb Z}_2$$ lattice gauge theories using two-component ultracold atoms in a double-well potential. For resonant periodic driving at the on-site interaction strength and an appropriate choice of the modulation parameters, the effective Floquet Hamiltonian exhibits $${\Bbb Z}_2$$ symmetry. We study the dynamics of the system for different initial states and critically contrast the observed evolution with a theoretical analysis of the full time-dependent Hamiltonian of the periodically driven lattice model. We reveal challenges that arise due to symmetry-breaking terms and outline potential pathways to overcome these limitations. Our results provide important insights for future studies of lattice gauge theories based on Floquet techniques.

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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 on reasonable request.

## Code availability

The code that supports the plots within this paper are available from the corresponding author on reasonable request.

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## Acknowledgements

We acknowledge insightful discussions with M. Dalmonte, A. Trombettoni and M. Lohse. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under project no. 277974659 via Research Unit FOR 2414 and under project no. 282603579 via DIP, the European Commission (UQUAM grant no. 5319278) and the Nanosystems Initiative Munich (NIM, grant no. EXC4). The work was further funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2111—390814868. Work in Brussels was supported by the FRS-FNRS (Belgium) and the ERC Starting Grant TopoCold. F.G. additionally acknowledges support by the Gordon and Betty Moore Foundation under the EPIQS programme and from the Technical University of Munich—Institute for Advanced Study, funded by the German Excellence Initiative and the European Union FP7 under grant agreement 291763, from the DFG grant no. KN 1254/1-1, and DFG TRR80 (Project F8). F.G. and E.D. acknowledge funding from Harvard-MIT CUA, AFOSR-MURI Quantum Phases of Matter (grant no. FA9550-14-1-0035), AFOSR-MURI: Photonic Quantum Matter (award no. FA95501610323) and DARPA DRINQS programme (award no. D18AC00014).

## Author information

Authors

### Contributions

C.S., F.G., N.G. and M.A. planned the experiment and performed theoretical calculations. C.S. and M.B. performed the experiment and analysed the data with M.A. All authors discussed the results and contributed to the writing of the paper.

### Corresponding author

Correspondence to Monika Aidelsburger.

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### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–13, text and references.

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Schweizer, C., Grusdt, F., Berngruber, M. et al. Floquet approach to 2 lattice gauge theories with ultracold atoms in optical lattices. Nat. Phys. 15, 1168–1173 (2019). https://doi.org/10.1038/s41567-019-0649-7

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• DOI: https://doi.org/10.1038/s41567-019-0649-7

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