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Topological quantum matter with ultracold gases in optical lattices

Abstract

Since the discovery of topological insulators, many topological phases have been predicted and realized in a range of different systems, providing both fascinating physics and exciting opportunities for devices. And although new materials are being developed and explored all the time, the prospects for probing exotic topological phases would be greatly enhanced if they could be realized in systems that were easily tuned. The flexibility offered by ultracold atoms could provide such a platform. Here, we review the tools available for creating topological states using ultracold atoms in optical lattices, give an overview of the theoretical and experimental advances and provide an outlook towards realizing strongly correlated topological phases.

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Figure 1: Measurement of the Chern number.
Figure 2: The Peierls substitution and the Aharonov–Bohm effect.
Figure 3: Exploiting a synthetic dimension.
Figure 4: Floquet engineering with cold atoms.

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Acknowledgements

The authors would like to acknowledge M. Aidelsburger, I. Bloch, L. Fallani and M. Mancini for providing experimental data. N.G. is financed by the FRS-FNRS Belgium and by the BSPO under PAI Project No. P7/18 DYGEST. This work has also been supported by the ERC synergy grant UQUAM.

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Goldman, N., Budich, J. & Zoller, P. Topological quantum matter with ultracold gases in optical lattices. Nature Phys 12, 639–645 (2016). https://doi.org/10.1038/nphys3803

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