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Measuring quantized circular dichroism in ultracold topological matter


The topology of two-dimensional materials traditionally manifests itself through the quantization of the Hall conductance, which is revealed in transport measurements1,2,3. Recently, it was predicted that topology can also give rise to a characteristic spectroscopic response on subjecting a Chern insulator to a circular drive: comparing the frequency-integrated depletion rates associated with drives of opposite orientation leads to a quantized response dictated by the topological Chern number of the populated Bloch band4,5. Here we experimentally demonstrate this intriguing topological effect using ultracold fermionic atoms in topological Floquet bands. In addition, our depletion-rate measurements also provide an experimental estimation of the Wannier-spread functional, a fundamental geometric property of Bloch bands related to the quantum metric6,7. Our results establish topological spectroscopic responses as a versatile probe, which could be applied to access the geometry and topology of many-body quantum systems, such as fractional Chern insulators8.

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All data files are available from the corresponding author on request. Source data for Figs. 3 and 4 and Supplementary Figs. 14 are provided in the Supplementary Information.

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The authors acknowledge discussions with N. R. Cooper, M. Dalmonte, A. Dauphin, A. G. Grushin, C. Repellin and P. Zoller, and they also thank P. Zoller for his insightful comments on the manuscript. This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via Research Unit FOR 2414 under project number 277974659 and via the Excellence Cluster ‘The Hamburg Centre for Ultrafast Imaging - Structure, Dynamics and Control of Matter at the Atomic Scale’ under project number 194651731. B.S.R. acknowledges financial support from the European Commission (Marie Curie Fellowship). Work in Brussels is supported by the FRS-FNRS (Belgium) and the ERC Starting Grant TopoCold. T.O. is supported by the Interdisciplinary Theoretical and Mathematical Sciences Program at RIKEN.

Author information

L.A., M.T., B.S.R. and N.F. obtained and analysed the experimental data, and also obtained numerical spectra, under the supervision of K.S. and C.W.; N.G. led the theoretical work; N.G., T.O. and D.T.T. performed various theoretical developments and calculations, including the study of timescale separation. All authors contributed to the interpretation of the results and to the writing of the manuscript.

Competing interests

The authors declare no competing interests.

Correspondence to Klaus Sengstock.

Supplementary information

Supplementary Information

Supplementary Text, Supplementary Figures 1–11 and Supplementary Reference.

Supplementary Dataset 1

Source data for Figs. 3 and 4 and Supplementary Figures 1–4.

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Further reading

Fig. 1: Quantized responses in topological matter.
Fig. 2: Measurement scheme.
Fig. 3: Chiral spectra of the Floquet bands.
Fig. 4: Spectroscopic signals across the topological phase diagram.