Letter | Published:

Enhancement and sign change of magnetic correlations in a driven quantum many-body system

Nature volume 553, pages 481485 (25 January 2018) | Download Citation


Periodic driving can be used to control the properties of a many-body state coherently and to realize phases that are not accessible in static systems. For example, exposing materials to intense laser pulses makes it possible to induce metal–insulator transitions, to control magnetic order and to generate transient superconducting behaviour well above the static transition temperature1,2,3,4,5,6. However, pinning down the mechanisms underlying these phenomena is often difficult because the response of a material to irradiation is governed by complex, many-body dynamics. For static systems, extensive calculations have been performed to explain phenomena such as high-temperature superconductivity7. Theoretical analyses of driven many-body Hamiltonians are more challenging, but approaches have now been developed, motivated by recent observations8,9,10. Here we report an experimental quantum simulation in a periodically modulated hexagonal lattice and show that antiferromagnetic correlations in a fermionic many-body system can be reduced, enhanced or even switched to ferromagnetic correlations (sign reversal). We demonstrate that the description of the many-body system using an effective Floquet–Hamiltonian with a renormalized tunnelling energy remains valid in the high-frequency regime by comparing the results to measurements in an equivalent static lattice. For near-resonant driving, the enhancement and sign reversal of correlations is explained by a microscopic model of the system in which the particle tunnelling and magnetic exchange energies can be controlled independently. In combination with the observed sufficiently long lifetimes of the correlations in this system, periodic driving thus provides an alternative way of investigating unconventional pairing in strongly correlated systems experimentally7,9,10.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    , & Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 82, 2731–2784 (2010)

  2. 2.

    & Nonlinear light-matter interaction at terahertz frequencies. Adv. Opt. Photonics 8, 401–464 (2016)

  3. 3.

    et al. Control of the electronic phase of a manganite by mode-selective vibrational excitation. Nature 449, 72–74 (2007)

  4. 4.

    et al. Structural and magnetic dynamics of a laser induced phase transition in FeRh. Phys. Rev. Lett. 108, 087201 (2012)

  5. 5.

    et al. Femtosecond switching of magnetism via strongly correlated spin–charge quantum excitations. Nature 496, 69–73 (2013)

  6. 6.

    et al. Possible light-induced superconductivity in K3C60 at high temperature. Nature 530, 461–464 (2016)

  7. 7.

    Correlated electrons in high-temperature superconductors. Rev. Mod. Phys. 66, 763–840 (1994)

  8. 8.

    , & Ultrafast and reversible control of the exchange interaction in Mott insulators. Nat. Commun. 6, 6708 (2015)

  9. 9.

    , , , & Enhancement of superexchange pairing in the periodically driven Hubbard model. Phys. Rev. B 96, 085104 (2017)

  10. 10.

    & η-pairing superfluid in periodically-driven fermionic Hubbard model with strong attraction. Phys. Rev. B 94, 174503 (2016)

  11. 11.

    & Periodically driven quantum systems: effective Hamiltonians and engineered gauge fields. Phys. Rev. X 4, 031027 (2014)

  12. 12.

    , & Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering. Adv. Phys. 64, 139–226 (2015)

  13. 13.

    et al. Quantum simulation of frustrated classical magnetism in triangular optical lattices. Science 333, 996–999 (2011)

  14. 14.

    et al. Creating state-dependent lattices for ultracold fermions by magnetic gradient modulation. Phys. Rev. Lett. 115, 073002 (2015)

  15. 15.

    Colloquium: Atomic quantum gases in periodically driven optical lattices. Rev. Mod. Phys. 89, 011004 (2017)

  16. 16.

    , , , & Coherent control of dressed matter waves. Phys. Rev. Lett. 102, 100403 (2009)

  17. 17.

    , & Direct observation of effective ferromagnetic domains of cold atoms in a shaken optical lattice. Nat. Phys. 9, 769–774 (2013)

  18. 18.

    et al. Photon-assisted tunneling in a biased strongly correlated Bose gas. Phys. Rev. Lett. 107, 095301 (2011)

  19. 19.

    , , , & Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms. Phys. Rev. Lett. 116, 205301 (2016)

  20. 20.

    et al. Controlling the Floquet state population and observing micromotion in a periodically driven two-body quantum system. Phys. Rev. A 96, 053602 (2017)

  21. 21.

    , & Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. 367, 96–124 (2016)

  22. 22.

    , , & Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017)

  23. 23.

    et al. Competition of spin and charge excitations in the one-dimensional Hubbard model. Phys. Rev. A 88, 063629 (2013)

  24. 24.

    et al. Thermodynamics and magnetic properties of the anisotropic 3D Hubbard model. Phys. Rev. Lett. 112, 115301 (2014)

  25. 25.

    , , , & Formation and dynamics of antiferromagnetic correlations in tunable optical lattices. Phys. Rev. Lett. 115, 260401 (2015)

  26. 26.

    & Interaction-dependent photon-assisted tunneling in optical lattices: a quantum simulator of strongly-correlated electrons and dynamical gauge fields. New J. Phys. 17, 103021 (2015)

  27. 27.

    & Effective Hamiltonians for rapidly driven many-body lattice systems: induced exchange interactions and density-dependent hoppings. Phys. Rev. Lett. 115, 075301 (2015)

  28. 28.

    , & Schrieffer-Wolff transformation for periodically driven systems: strongly correlated systems with artificial gauge fields. Phys. Rev. Lett. 116, 125301 (2016)

  29. 29.

    et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008)

  30. 30.

    et al. Controlling correlated tunneling and superexchange interactions with ac-driven optical lattices. Phys. Rev. Lett. 107, 210405 (2011)

  31. 31.

    , , , & Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice. Nature 483, 302–305 (2012)

  32. 32.

    , , , & Short-range quantum magnetism of ultracold fermions in an optical lattice. Science 340, 1307–1310 (2013)

  33. 33.

    et al. Artificial graphene with tunable interactions. Phys. Rev. Lett. 111, 185307 (2013)

Download references


We thank D. Abanin, D. Greif, D. Jaksch, M. Landini, Y. Murakami, N. Tsuji, P. Werner and W. Zwerger for discussions. We acknowledge SNF (Project Number 200020_169320 and NCCR-QSIT), Swiss State Secretary for Education, Research and Innovation Contract No. 15.0019 (QUIC) and ERC advanced grant TransQ (Project Number 742579) for funding.

Author information


  1. Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland

    • Frederik Görg
    • , Michael Messer
    • , Kilian Sandholzer
    • , Gregor Jotzu
    • , Rémi Desbuquois
    •  & Tilman Esslinger
  2. Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany

    • Gregor Jotzu


  1. Search for Frederik Görg in:

  2. Search for Michael Messer in:

  3. Search for Kilian Sandholzer in:

  4. Search for Gregor Jotzu in:

  5. Search for Rémi Desbuquois in:

  6. Search for Tilman Esslinger in:


All authors contributed extensively to the work presented in this manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Tilman Esslinger.

Reviewer Information Nature thanks J. Freericks and D. Huse for their contribution to the peer review of this work.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

About this article

Publication history







By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.