Letter | Published:

Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models

Nature volume 534, pages 667670 (30 June 2016) | Download Citation

Abstract

Spin models are the prime example of simplified many-body Hamiltonians used to model complex, strongly correlated real-world materials1. However, despite the simplified character of such models, their dynamics often cannot be simulated exactly on classical computers when the number of particles exceeds a few tens. For this reason, quantum simulation2 of spin Hamiltonians using the tools of atomic and molecular physics has become a very active field over the past years, using ultracold atoms3 or molecules4 in optical lattices, or trapped ions5. All of these approaches have their own strengths and limitations. Here we report an alternative platform for the study of spin systems, using individual atoms trapped in tunable two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100 per cent. When excited to high-energy Rydberg D states, the atoms undergo strong interactions whose anisotropic character opens the way to simulating exotic matter6. We illustrate the versatility of our system by studying the dynamics of a quantum Ising-like spin-1/2 system in a transverse field with up to 30 spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects on the dynamics, we find excellent agreement with ab initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D states has a measurable influence7,8. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.

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References

  1. 1.

    Interacting Electrons and Quantum Magnetism (Springer, New York, 1994)

  2. 2.

    , & Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014)

  3. 3.

    , & Quantum simulations with ultracold quantum gases. Nature Phys. 8, 267–276 (2012)

  4. 4.

    et al. Observation of dipolar spin-exchange interactions with lattice-confined polar molecules. Nature 501, 521–525 (2013)

  5. 5.

    & Quantum simulations with trapped ions. Nature Phys. 8, 277–284 (2012)

  6. 6.

    et al. Quantum spin-ice and dimer models with Rydberg atoms. Phys. Rev. X 4, 041037 (2014)

  7. 7.

    , & Magic distances in the blockade mechanism of Rydberg P and D states. Phys. Rev. A 91, 023411 (2015)

  8. 8.

    et al. Dipolar dephasing of Rydberg D-state polaritons. Phys. Rev. Lett. 115, 083602 (2015)

  9. 9.

    , & Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313–2363 (2010)

  10. 10.

    , , , & A Rydberg quantum simulator. Nature Phys. 6, 382–388 (2010)

  11. 11.

    et al. Demonstration of a strong Rydberg blockade in three-atom systems with anisotropic interactions. Phys. Rev. Lett. 112, 183002 (2014)

  12. 12.

    , , , & Direct measurement of the van der Waals interaction between two Rydberg atoms. Phys. Rev. Lett. 110, 263201 (2013)

  13. 13.

    et al. Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries. Phys. Rev. X 4, 021034 (2014)

  14. 14.

    , , & Observation of coherent many-body Rabi oscillations. Nature Phys. 8, 790–794 (2012)

  15. 15.

    et al. Atomic Fock state preparation using Rydberg blockade. Phys. Rev. Lett. 112, 043602 (2014)

  16. 16.

    , , & Coherence and Rydberg blockade of atomic ensemble qubits. Phys. Rev. Lett. 115, 093601 (2015)

  17. 17.

    et al. Microscopic characterization of scalable coherent Rydberg superatoms. Phys. Rev. X 5, 031015 (2015)

  18. 18.

    & Entropic enhancement of spatial correlations in a laser-driven Rydberg gas. Phys. Rev. A 86, 013408 (2012)

  19. 19.

    , & Spatial correlations of Rydberg excitations in optically driven atomic ensembles. Phys. Rev. A 87, 053414 (2013)

  20. 20.

    et al. Observation of spatially ordered structures in a two-dimensional Rydberg gas. Nature 491, 87–91 (2012)

  21. 21.

    et al. Universal scaling in a strongly interacting Rydberg gas. Phys. Rev. A 80, 033422 (2009)

  22. 22.

    , , , & Rapid production of uniformly-filled arrays of neutral atoms. Phys. Rev. Lett. 115, 073003 (2015)

  23. 23.

    & Efficient collisional blockade loading of single atom into a tight microtrap. New J. Phys. 17, 073011 (2015)

  24. 24.

    et al. From molecular spectra to a density shift in dense Rydberg gases. Nature Commun. 5, 4546 (2014)

  25. 25.

    , & Thermalization of a strongly interacting closed spin system: from coherent many-body dynamics to a Fokker-Planck equation. Phys. Rev. Lett. 108, 110603 (2012)

  26. 26.

    et al. Quantum correlations and entanglement in far-from-equilibrium spin systems. Phys. Rev. A 90, 063622 (2014)

  27. 27.

    et al. Coherent excitation transfer in a spin chain of three Rydberg atoms. Phys. Rev. Lett. 114, 113002 (2015)

  28. 28.

    et al. Complete devil’s staircase and crystal-superfluid transitions in a dipolar XXZ spin chain: a trapped ion quantum simulation. New J. Phys. 12, 113037 (2010)

  29. 29.

    et al. Realization of a quantum integer-spin chain with controllable interactions. Phys. Rev. X 5, 021026 (2015)

  30. 30.

    et al. Topological bands with a Chern number C = 2 by dipolar exchange interactions. Phys. Rev. A 91, 053617 (2015)

  31. 31.

    & Correcting detection errors in quantum state engineering through data processing. New J. Phys. 14, 053053 (2012)

  32. 32.

    et al. Many-body interferometry of a Rydberg-dressed spin lattice. (2016)

  33. 33.

    et al. Crystallization in Ising quantum magnets. Science 347, 1455–1458 (2015)

  34. 34.

    , , , & Effects of molecular resonances on Rydberg blockade. Phys. Rev. A 92, 063419 (2015)

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Acknowledgements

We thank H. Busche for contributions in the early stages of the experiment, I. Lesanovsky, H. P. Büchler and T. Pohl for discussions, and Y. Sortais for a reading of the manuscript. This work benefited from financial support by the EU (FET-Open Xtrack Project HAIRS, H2020 FET-PROACT Project RySQ, and EU Marie-Curie Program ITN COHERENCE FP7-PEOPLE-2010-ITN-265031 (H.L.)), by the ‘PALM’ Labex (project QUANTICA) and by the Région Île-de-France in the framework of DIM Nano-K.

Author information

Author notes

    • Henning Labuhn
    •  & Daniel Barredo

    These authors contributed equally to this work.

Affiliations

  1. Laboratoire Charles Fabry, Institut d’Optique, CNRS, Université Paris Sud 11, 2 avenue Augustin Fresnel, 91127 Palaiseau Cedex, France

    • Henning Labuhn
    • , Daniel Barredo
    • , Sylvain Ravets
    • , Sylvain de Léséleuc
    • , Thierry Lahaye
    •  & Antoine Browaeys
  2. Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, and International Institute of Physics, Natal-RN, Brazil

    • Tommaso Macrì

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Contributions

All authors made critical contributions to the work, discussed the results, and contributed to the writing of the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Thierry Lahaye.

Reviewer Information Nature thanks C. F. Roos and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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https://doi.org/10.1038/nature18274

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