Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

A Mott insulator of fermionic atoms in an optical lattice


Strong interactions between electrons in a solid material can lead to surprising properties. A prime example is the Mott insulator, in which suppression of conductivity occurs as a result of interactions rather than a filled Bloch band1. Proximity to the Mott insulating phase in fermionic systems is the origin of many intriguing phenomena in condensed matter physics2, most notably high-temperature superconductivity3. The Hubbard model4, which encompasses the essential physics of the Mott insulator, also applies to quantum gases trapped in an optical lattice5,6. It is therefore now possible to access this regime with tools developed in atomic physics. However, an atomic Mott insulator has so far been realized only with a gas of bosons7, which lack the rich and peculiar nature of fermions. Here we report the formation of a Mott insulator of a repulsively interacting two-component Fermi gas in an optical lattice. It is identified by three features: a drastic suppression of doubly occupied lattice sites, a strong reduction of the compressibility inferred from the response of double occupancy to an increase in atom number, and the appearance of a gapped mode in the excitation spectrum. Direct control of the interaction strength allows us to compare the Mott insulating regime and the non-interacting regime without changing tunnel-coupling or confinement. Our results pave the way for further studies of the Mott insulator, including spin-ordering and ultimately the question of d-wave superfluidity6,8.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout

Figure 1: Energy spectrum of a Fermi gas in an optical lattice with an underlying confining potential.
Figure 2: Double occupancy in the non-interacting and Mott insulating regimes.
Figure 3: The transition to an incompressible sample.
Figure 4: Emergence of a gapped mode.


  1. Mott, N. F. Metal–Insulator Transitions (Taylor & Francis, 1990)

    Book  Google Scholar 

  2. Imada, M., Fujimori, A. & Tokura, Y. Metal–insulator transitions. Rev. Mod. Phys. 70, 1039–1263 (1998)

    Article  CAS  ADS  Google Scholar 

  3. Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006)

    Article  CAS  ADS  Google Scholar 

  4. Hubbard, J. Electron correlations in narrow energy bands. Proc. R. Soc. Lond. A 276, 238–257 (1963)

    Article  ADS  Google Scholar 

  5. Jaksch, D., Bruder, C., Cirac, J. I., Gardiner, C. W. & Zoller, P. Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108–3111 (1998)

    Article  CAS  ADS  Google Scholar 

  6. Hofstetter, W., Cirac, J. I., Zoller, P., Demler, E. & Lukin, M. D. High-temperature superfluidity of fermionic atoms in optical lattices. Phys. Rev. Lett. 89, 220407 (2002)

    Article  CAS  ADS  Google Scholar 

  7. Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002)

    Article  CAS  ADS  Google Scholar 

  8. Trebst, S., Schollwöck, U., Troyer, M. & Zoller, P. d-wave resonating valence bond states of fermionic atoms in optical lattices. Phys. Rev. Lett. 96, 250402 (2006)

    Article  ADS  Google Scholar 

  9. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008)

    Article  CAS  ADS  Google Scholar 

  10. Giorgini, L., Pitaevskii, L. P. & Stringari, S. Theory of ultracold Fermi gases. Preprint at 〈〉 (2007)

  11. Georges, A. in Ultracold Fermi Gases (eds Inguscio, M., Ketterle, W. & Salomon, C.) 477–533 (IOS Press, 2007)

    Google Scholar 

  12. Köhl, M., Moritz, H., Stöferle, T., Günter, K. & Esslinger, T. Fermionic atoms in a three dimensional optical lattice: observing Fermi surfaces, dynamics, and interactions. Phys. Rev. Lett. 94, 080403 (2005)

    Article  ADS  Google Scholar 

  13. Stöferle, T., Moritz, H., Günter, K., Köhl, M. & Esslinger, T. Molecules of fermionic atoms in an optical lattice. Phys. Rev. Lett. 96, 030401 (2006)

    Article  ADS  Google Scholar 

  14. Chin, J. K. et al. Evidence for superfluidity of ultracold fermions in an optical lattice. Nature 443, 961–964 (2006)

    Article  CAS  ADS  Google Scholar 

  15. Rom, T. et al. Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice. Nature 444, 733–736 (2006)

    Article  CAS  ADS  Google Scholar 

  16. Strohmaier, N. et al. Interaction-controlled transport of an ultracold Fermi gas. Phys. Rev. Lett. 99, 220601 (2007)

    Article  ADS  Google Scholar 

  17. Helmes, R. W., Costi, T. A. & Rosch, A. Mott transition of fermionic atoms in a three-dimensional optical trap. Phys. Rev. Lett. 100, 056403 (2008)

    Article  CAS  ADS  Google Scholar 

  18. Rigol, M., Muramatsu, A., Batrouni, G. G. & Scalettar, R. T. Local quantum criticality in confined fermions on optical lattices. Phys. Rev. Lett. 91, 130403 (2003)

    Article  CAS  ADS  Google Scholar 

  19. Georges, A., Kotliar, G., Krauth, W. & Rozenberg, M. J. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev. Mod. Phys. 68, 13–125 (1996)

    Article  CAS  ADS  MathSciNet  Google Scholar 

  20. Köhl, M. Thermometry of fermionic atoms in an optical lattice. Phys. Rev. A 73, 031601(R) (2006)

    Article  ADS  Google Scholar 

  21. Gebhard, F. The Mott Metal–Insulator Transition—Models and Methods (Springer, 1997)

    Google Scholar 

  22. Gerbier, F. Boson Mott insulators at finite temperatures. Phys. Rev. Lett. 99, 120405 (2007)

    Article  ADS  Google Scholar 

  23. Gerbier, F., Fölling, S., Widera, A., Mandel, O. & Bloch, I. Probing number squeezing of ultracold atoms across the superfluid–Mott insulator transition. Phys. Rev. Lett. 96, 090401 (2006)

    Article  ADS  Google Scholar 

  24. Brinkman, W. F. & Rice, T. M. Single-particle excitations in magnetic insulators. Phys. Rev. B 2, 1324–1338 (1970)

    Article  ADS  Google Scholar 

  25. Stöferle, T., Moritz, H., Schori, C., Köhl, M. & Esslinger, T. Transition from a strongly interacting 1D superfluid to a Mott insulator. Phys. Rev. Lett. 92, 130403 (2004)

    Article  ADS  Google Scholar 

  26. Kollath, C., Iucci, A., McCulloch, I. P. & Giamarchi, T. Modulation spectroscopy with ultracold fermions in an optical lattice. Phys. Rev. A 74, 041604(R) (2006)

    Article  ADS  Google Scholar 

  27. Huber, S. D., Theiler, B., Altman, E. & Blatter, G. Amplitude mode in the quantum phase model. Phys. Rev. Lett. 100, 050404 (2008)

    Article  CAS  ADS  Google Scholar 

  28. Regal, C. A. & Jin, D. S. Measurement of positive and negative scattering lengths in a Fermi gas of atoms. Phys. Rev. Lett. 90, 230404 (2003)

    Article  CAS  ADS  Google Scholar 

Download references


We thank J. Blatter, S. Huber, M. Köhl, C. Kollath, L. Pollet, N. Prokof’ev, M. Rigol, M. Sigrist, M. Troyer and W. Zwerger for discussions. Funding was provided by the Swiss National Science Foundation (SNF), the EU projects Optical Lattices and Quantum Information (OLAQUI) and Scalable Quantum Computing with Light and Atoms (SCALA) and the Quantum Science and Technology (QSIT) project of ETH Zurich.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Henning Moritz.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Jördens, R., Strohmaier, N., Günter, K. et al. A Mott insulator of fermionic atoms in an optical lattice. Nature 455, 204–207 (2008).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


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.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing