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# Thermodynamics of a deeply degenerate SU(N)-symmetric Fermi gas

## Abstract

Many-body quantum systems can exhibit a striking degree of symmetry unparallelled in their classical counterparts. In real materials SU(N) symmetry is an idealization, but this symmetry is pristinely realized in fully controllable ultracold alkaline-earth atomic gases. Here, we study an SU(N)-symmetric Fermi liquid of 87Sr atoms, where N can be tuned to be as large as 10. In the deeply degenerate regime, we show through precise measurements of density fluctuations and expansion dynamics that the large N of spin states under SU(N) symmetry leads to pronounced interaction effects in a system with a nominally negligible interaction parameter. Accounting for these effects, we demonstrate thermometry accurate to 1% of the Fermi energy. We also demonstrate record speed for preparing degenerate Fermi seas enabled by the SU(N)-symmetric interactions, reaching T/TF = 0.22 with 10 nuclear spin states in 0.6 s working with a laser-cooled sample. This, along with the introduction of a new spin polarizing method, enables the operation of a three-dimensional optical lattice clock in the band insulating regime.

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Nature Communications Open Access 31 March 2021

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## Data availability

The datasets generated and analysed during the current study are available from the corresponding author L.S. on reasonable request.

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## Acknowledgements

We thank T. Bothwell, C. Kennedy, E. Oelker and J. Robinson for discussions and technical contributions. We also thank J. Thompson and C. Kennedy for reading the manuscript. This work is supported by NIST, DARPA, and AFOSR grant nos. FA9550-19-1-0275 and FA9550-18-1-0319, and NSF grant no. PHYS-1734006. C.S. thanks the Humboldt Foundation for support.

## Author information

Authors

### Contributions

L.S., C.S., R.B.H., A.G., L.Y., W.R.M. and J.Y. contributed to the experimental measurements. T.B. and A.M.R. developed the theoretical model. All authors discussed the results, contributed to the data analysis and worked together on the manuscript.

### Corresponding authors

Correspondence to Lindsay Sonderhouse or Jun Ye.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Stefano Giorgini, Florian Schreck and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Sonderhouse, L., Sanner, C., Hutson, R.B. et al. Thermodynamics of a deeply degenerate SU(N)-symmetric Fermi gas. Nat. Phys. 16, 1216–1221 (2020). https://doi.org/10.1038/s41567-020-0986-6

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• DOI: https://doi.org/10.1038/s41567-020-0986-6

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