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.

Interaction and filling-induced quantum phases of dual Mott insulators of bosons and fermions


Many-body effects are at the very heart of diverse phenomena found in condensed-matter physics. One striking example is the Mott-insulator phase, where conductivity is suppressed as a result of a strong repulsive interaction. Advances in cold-atom physics have led to the realization of the Mott-insulating phases of atoms in an optical lattice, mimicking the corresponding condensed-matter systems. Here, we explore an exotic strongly-correlated system of interacting dual Mott insulators of bosons and fermions. We find that an interspecies interaction between bosons and fermions drastically modifies each of the Mott insulators, causing effects that include melting, generation of composite particles, an anti-correlated phase and complete phase separation. Comparison between the experimental results and numerical simulations indicate intrinsic adiabatic heating and cooling for the attractively and repulsively interacting dual Mott insulators, respectively.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Schematic illustration of effects of interspecies interaction and filling on dual Mott insulators of bosons and fermions.
Figure 2: Photoassociation and occupancy measurements in an optical lattice.
Figure 3: Occupancy measurements and numerical simulation of occupancy distributions.
Figure 4: Modulation spectroscopy of mixed Mott insulator.
Figure 5: Various types of composite particles in the attractively interacting system.
Figure 6: Thermodynamics of repulsively and attractively interacting dual Mott insulators.


  1. 1

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

    ADS  Google Scholar 

  2. 2

    Jaksch, D. & Zoller, P. The cold atom Hubbard toolbox. Ann. Phys. 315, 52–79 (2005).

    ADS  Article  Google Scholar 

  3. 3

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

    ADS  Article  Google Scholar 

  4. 4

    Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid–insulator transition. Phys. Rev. B 40, 546–570 (1989).

    ADS  Article  Google Scholar 

  5. 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).

    ADS  Article  Google Scholar 

  6. 6

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

    ADS  Article  Google Scholar 

  7. 7

    Spielman, I. B., Phillips, W. D. & Porto, J. V. Mott-insulator transition in a two-dimensional atomic Bose gas. Phys. Rev. Lett. 98, 080404 (2007).

    ADS  Article  Google Scholar 

  8. 8

    Jördens, R., Strohmaier, N., Günter, K., Moritz, H. & Esslinger, T. A Mott insulator of fermionic atoms in an optical lattice. Nature 455, 204–207 (2008).

    ADS  Article  Google Scholar 

  9. 9

    Schneider, U. et al. Metallic and insulating phases of repulsively interacting fermions in a 3D optical lattice. Science 322, 1520–1525 (2008).

    ADS  Article  Google Scholar 

  10. 10

    Campbell, G. K. et al. Imaging the Mott insulator shells by using atomic clock shifts. Science 313, 649–652 (2006).

    ADS  Article  Google Scholar 

  11. 11

    Fölling, S., Widera, A., Müller, T., Gerbier, F. & Bloch, I. Formation of spatial shell structure in the superfluid to Mott insulator transition. Phys. Rev. Lett. 97, 060403 (2006).

    ADS  Article  Google Scholar 

  12. 12

    Gemelke, N., Zhang, X., Hung, C-L. & Chin, C. In situ observation of incompressible Mott-insulating domains in ultracold atomic gases. Nature 460, 995–998 (2009).

    ADS  Article  Google Scholar 

  13. 13

    Bakr, W. S. et al. Probing the superfluid-to-Mott insulator transition at the single-atom level. Science 329, 547–550 (2010).

    ADS  Article  Google Scholar 

  14. 14

    Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010).

    ADS  Article  Google Scholar 

  15. 15

    Titvinidze, I., Snoek, M. & Hofstetter, W. Supersolid Bose–Fermi mixtures in optical lattices. Phys. Rev. Lett. 100, 100401 (2008).

    ADS  Article  Google Scholar 

  16. 16

    Lewenstein, M., Santos, L., Baranov, M. A. & Fehrmann, H. Atomic Bose–Fermi mixtures in an optical lattice. Phys. Rev. Lett. 92, 050401 (2004).

    ADS  Article  Google Scholar 

  17. 17

    Hubener, A., Snoek, M. & Hofstetter, W. Magnetic phases of two-component ultracold bosons in an optical lattice. Phys. Rev. B 80, 245109 (2009).

    ADS  Article  Google Scholar 

  18. 18

    Capogrosso-Sansone, B., Söyler, Ş. G., Prokof’ev, N. V. & Svistunov, B. V. Critical entropies for magnetic ordering in bosonic mixtures on a lattice. Phys. Rev. A 81, 053622 (2010).

    ADS  Article  Google Scholar 

  19. 19

    Iskin, M. & Sá de Melo, C. A. R. Superfluid and insulating phases of fermion mixtures in optical lattices. Phys. Rev. Lett. 99, 080403 (2007).

    ADS  Article  Google Scholar 

  20. 20

    Günter, K., Stöferle, T., Moritz, H., Köhl, M. & Esslinger, T. Bose–Fermi mixtures in a three-dimensional optical lattice. Phys. Rev. Lett. 96, 180402 (2006).

    ADS  Article  Google Scholar 

  21. 21

    Ospelkaus, S. et al. Localization of bosonic atoms by fermionic impurities in a three-dimensional optical lattice. Phys. Rev. Lett. 96, 180403 (2006).

    ADS  Article  Google Scholar 

  22. 22

    Best, T. et al. Role of interactions in 87Rb–40K Bose–Fermi mixtures in a 3d optical lattice. Phys. Rev. Lett. 102, 030408 (2009).

    ADS  Article  Google Scholar 

  23. 23

    Catani, J., De Sarlo, L., Barontini, G., Minardi, F. & Inguscio, M. Degenerate Bose–Bose mixture in a three-dimensional optical lattice. Phys. Rev. A 77, 011603 (2008).

    ADS  Article  Google Scholar 

  24. 24

    Weld, D. M. et al. Spin gradient thermometry for ultracold atoms in optical lattices. Phys. Rev. Lett. 103, 245301 (2009).

    ADS  Article  Google Scholar 

  25. 25

    Gadway, B., Pertot, D., Reimann, R. & Schneble, D. Superfluidity of interacting bosonic mixtures in optical lattices. Phys. Rev. Lett. 105, 045303 (2010).

    ADS  Article  Google Scholar 

  26. 26

    Taglieber, M., Voigt, A-C., Aoki, T., Hänsch, T. W. & Dieckmann, K. Quantum degenerate two-species Fermi–Fermi mixture coexisting with a Bose–Einstein condensate. Phys. Rev. Lett. 100, 010401 (2008).

    ADS  Article  Google Scholar 

  27. 27

    Taie, S. et al. Realization of a SU(2)×SU(6) system of fermions in a cold atomic gas. Phys. Rev. Lett. 105, 190401 (2010).

    ADS  Article  Google Scholar 

  28. 28

    Kitagawa, M. et al. Two-color photoassociation spectroscopy of ytterbium atoms and the precise determinations of s-wave scattering lengths. Phys. Rev. A 77, 012719 (2008).

    ADS  Article  Google Scholar 

  29. 29

    Batrouni, G. G. et al. Mott domains of bosons confined on optical lattices. Phys. Rev. Lett. 89, 117203 (2002).

    ADS  Article  Google Scholar 

  30. 30

    Rom, T. et al. State selective production of molecules in optical lattices. Phys. Rev. Lett. 93, 073002 (2004).

    ADS  Article  Google Scholar 

  31. 31

    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).

    ADS  Article  Google Scholar 

  32. 32

    Greif, D., Tarruell, L., Uehlinger, T., Jördens, R. & Esslinger, T. Probing nearest-neighbor correlations of ultracold fermions in an optical lattice. Phys. Rev. Lett. 106, 145302 (2011).

    ADS  Article  Google Scholar 

  33. 33

    Richardson, R. C. The Pomeranchuk effect. Rev. Mod. Phys. 69, 683–690 (1997).

    ADS  Article  Google Scholar 

  34. 34

    Werner, F., Parcollet, O., Georges, A. & Hassan, S. R. Interaction-induced adiabatic cooling and antiferromagnetism of cold fermions in optical lattices. Phys. Rev. Lett. 95, 056401 (2005).

    ADS  Article  Google Scholar 

  35. 35

    Cazalilla, M. A., Ho, A. F. & Ueda, M. Ultracold gases of ytterbium: Ferromagnetism and Mott states in an SU(6) fermi system. New J. Phys. 11, 103033 (2009).

    ADS  Article  Google Scholar 

  36. 36

    Hazzard, K. R. A., Gurarie, V., Hermele, M. & Rey, A. M. High temperature thermodynamics of fermionic alkaline earth atoms in optical lattices. Preprint at (2005).

  37. 37

    Cramer, M. et al. Do mixtures of bosonic and fermionic atoms adiabatically heat up in optical lattices? Phys. Rev. Lett. 100, 140409 (2008).

    ADS  Article  Google Scholar 

  38. 38

    Snoek, M., Titvinidze, I., Bloch, I. & Hofstetter, W. Effect of interactions on harmonically confined Bose–Fermi mixtures in optical lattices. Phys. Rev. Lett. 106, 155301 (2011).

    ADS  Article  Google Scholar 

  39. 39

    Fukuhara, T., Sugawa, S., Takasu, Y. & Takahashi, Y. All-optical formation of quantum degenerate mixtures. Phys. Rev. A 79, 021601 (2009).

    ADS  Article  Google Scholar 

  40. 40

    Fukuhara, T., Sugawa, S., Sugimoto, M., Taie, S. & Takahashi, Y. Mott insulator of ultracold alkaline-earth-metal-like atoms. Phys. Rev. A 79, 041604 (2009).

    ADS  Article  Google Scholar 

  41. 41

    Krauth, W., Caffarel, M. & Bouchaud, J-P. Gutzwiller wave function for a model of strongly interacting bosons. Phys. Rev. B 45, 3137–3140 (1992).

    ADS  Article  Google Scholar 

  42. 42

    Lühmann, D-S., Bongs, K., Sengstock, K. & Pfannkuche, D. Self-trapping of bosons and fermions in optical lattices. Phys. Rev. Lett. 101, 050402 (2008).

    ADS  Article  Google Scholar 

Download references


We acknowledge S. Uetake, T. Fukuhara, S. Sugimoto, Y. Takasu and H. Wayama for their experimental help and J. Doyle for careful reading of the manuscript. This work is supported by the Grant-in-Aid for Scientific Research of JSPS (No. 18204035, 21102005C01 (Quantum Cybernetics)), GCOE Program ‘The Next Generation of Physics, Spun from Universality and Emergence’ from MEXT of Japan, and World- Leading Innovative R&D on Science and Technology (FIRST). S.S and S.T. acknowledge support from JSPS.

Author information




S.S., S.T. and R.Y. performed the experiment. K.I. and M.Y. performed the theoretical analysis. Y.T. supervised the whole project. All the authors discussed the results and wrote the manuscript.

Corresponding author

Correspondence to Seiji Sugawa.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 303 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sugawa, S., Inaba, K., Taie, S. et al. Interaction and filling-induced quantum phases of dual Mott insulators of bosons and fermions. Nature Phys 7, 642–648 (2011).

Download citation

Further reading


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