Letter

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

Received:
Accepted:
Published online:

Abstract

Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-temperature superconductivity1. The Hubbard model—a simplified representation of fermions moving on a periodic lattice—is thought to describe the essential details of copper oxide superconductivity2. This model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realize the Hubbard model with readily tunable parameters, and thus provide a platform for the systematic exploration of its phase diagram3,4. Realization of strongly correlated phases, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry5. Here we demonstrate spin-sensitive Bragg scattering of light to measure AFM spin correlations in a realization of the three-dimensional Hubbard model at temperatures down to 1.4 times that of the AFM phase transition. This temperature regime is beyond the range of validity of a simple high-temperature series expansion, which brings our experiment close to the limit of the capabilities of current numerical techniques, particularly at metallic densities. We reach these low temperatures using a compensated optical lattice technique6, in which the confinement of each lattice beam is compensated by a blue-detuned laser beam. The temperature of the atoms in the lattice is deduced by comparing the light scattering to determinant quantum Monte Carlo simulations7 and numerical linked-cluster expansion8 calculations. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, would open avenues for producing and characterizing other novel quantum states of matter, such as the pseudogap regime and correlated metallic states of the two-dimensional Hubbard model.

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Acknowledgements

This work was supported under ARO grant no. W911NF-13-1-0018 with funds from the DARPA OLE programme, NSF, ONR, the Welch Foundation (grant no. C-1133), and an ARO-MURI grant no. W911NF-14-1-003. T.P. acknowledges support from CNPq, FAPERJ, and the INCT on Quantum Information. R.T.S. acknowledges support from the Office of the President of the University of California.

Author information

Author notes

    • Russell A. Hart
    •  & Pedro M. Duarte

    These authors contributed equally to this work.

Affiliations

  1. Department of Physics and Astronomy and Rice Quantum Institute, Rice University, 6100 Main Street, Houston, Texas 77005, USA

    • Russell A. Hart
    • , Pedro M. Duarte
    • , Tsung-Lin Yang
    • , Xinxing Liu
    •  & Randall G. Hulet
  2. Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68.528, Rio de Janeiro RJ, 21941-972, Brazil

    • Thereza Paiva
  3. Department of Physics and Astronomy, San Jose State University, 1 Washington Square, San Jose, California 95192, USA

    • Ehsan Khatami
  4. Department of Physics, University of California, 1 Shields Avenue, Davis, California 95616, USA

    • Richard T. Scalettar
  5. Department of Physics, The Ohio State University, 191 West Woodruff Avenue, Columbus, Ohio 43210, USA

    • Nandini Trivedi
  6. Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

    • David A. Huse

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Contributions

The experimental work was performed by R.A.H., P.M.D., T.-L.Y., X.L. and R.G.H., while T.P., E.K., P.M.D., R.T.S., N.T. and D.A.H. performed the theory needed to extract temperatures from the data and provided overall theoretical guidance. All authors contributed to the writing of the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Randall G. Hulet.

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