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Angle-resolved photoemission spectroscopy of a Fermi–Hubbard system

Abstract

Angle-resolved photoemission spectroscopy (ARPES) measures the single-particle excitations of a many-body quantum system with energy and momentum resolution, providing detailed information about strongly interacting materials1. ARPES directly probes fermion pairing, and hence is a natural technique to study the development of superconductivity in systems ranging from high-temperature superconductors to unitary Fermi gases. In these systems, a remnant gap-like feature persists in the normal state2. Developing a quantitative understanding of these so-called pseudogap regimes may elucidate details about the pairing mechanisms that lead to superconductivity, but this is difficult in real materials partly because the microscopic Hamiltonian is not known. Here, we report on the development of ARPES to study strongly interacting fermions in an optical lattice using a quantum gas microscope. We benchmark the technique by measuring the occupied single-particle spectral function of an attractive Fermi–Hubbard system across the BCS–BEC crossover and comparing the results to those of quantum Monte Carlo calculations. We find evidence for a pseudogap that opens well above the expected critical temperature for superfluidity. This technique may also be applied to the doped repulsive Hubbard model, which is expected to exhibit a pseudogap at temperatures close to those achieved in recent experiments3.

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Fig. 1: ARPES technique and raw data.
Fig. 2: Trap-averaged spectral function.
Fig. 3: Occupied spectral function versus interaction.
Fig. 4: Occupied spectral function versus temperature at strong coupling.

Data availability

The data displayed in Figs. 14 are available online at https://doi.org/10.17605/OSF.IO/UEFP8. Supporting data generated during the current study are available from the corresponding author on reasonable request.

Code availability

The code to reproduce the analysis in this study is available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the NSF (grant no. DMR-1607277), the David and Lucile Packard Foundation (grant no. 2016-65128) and the AFOSR Young Investigator Research Program (grant no. FA9550-16-1-0269). T.P.D. and E.W.H. acknowledge support from the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract no. DE-AC02-76SF00515. Computational work was performed on the Sherlock cluster at Stanford University.

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Contributions

P.T.B. and W.S.B. conceived the experiment. P.T.B., E.G.-S. and B.M.S. collected the experimental data and performed the data analysis. E.W.H. and T.P.D. performed the quantum Monte Carlo calculations. T.P.D. and W.S.B. supervised the project. All authors contributed to the writing of the manuscript.

Corresponding author

Correspondence to Waseem S. Bakr.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary text, Figs. 1–7 and references.

Supplementary Data

Text files containing the data plotted in Figs. 1–4.

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Brown, P.T., Guardado-Sanchez, E., Spar, B.M. et al. Angle-resolved photoemission spectroscopy of a Fermi–Hubbard system. Nat. Phys. 16, 26–31 (2020). https://doi.org/10.1038/s41567-019-0696-0

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