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.

In situ observation of incompressible Mott-insulating domains in ultracold atomic gases


The observation of the superfluid to Mott insulator phase transition of ultracold atoms in optical lattices1 was an enabling discovery in experimental many-body physics, providing the first tangible example of a quantum phase transition (one that occurs even at zero temperature) in an ultracold atomic gas. For a trapped gas, the spatially varying local chemical potential gives rise to multiple quantum phases within a single sample, complicating the interpretation of bulk measurements1,2,3,4,5. Here we report spatially resolved, in-situ imaging of a two-dimensional ultracold atomic gas as it crosses the superfluid to Mott insulator transition, providing direct access to individual characteristics of the insulating, superfluid and normal phases. We present results for the local compressibility in all phases, observing a strong suppression in the insulator domain and suppressed density fluctuations for the Mott insulator, in accordance with the fluctuation–dissipation theorem. Furthermore, we obtain a direct measure of the finite temperature of the system. Taken together, these methods enable a complete characterization of multiple phases in a strongly correlated Bose gas, and of the interplay between quantum and thermal fluctuations in the quantum critical regime.

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

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: False-colour absorption images and line cuts along major axis of density profiles for N = 7,500 ultracold caesium atoms at scattering length a = 310 a B in 2D optical lattices.
Figure 2: Histograms of density profiles in the Mott-insulator regime and the superfluid regime.
Figure 3: Extraction of compressibility from density profiles.
Figure 4: The fluctuation of local density extracted from a set of eleven absorption images in the weak and deep lattice regimes.


  1. Greiner, M., Mandel, O., Esslinger, T., Hansch, 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 

  2. Spielman, I. B., Phillips, W. D. & Porto, J. V. Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition. Phys. Rev. Lett. 100, 120402 (2008)

    Article  CAS  ADS  Google Scholar 

  3. Kohl, M., Moritz, H., Stoferle, T., Schori, C. & Esslinger, T. Superfluid to Mott insulator transition in one, two and three dimensions. J. Low-Temp. Phys. 138, 635–644 (2005)

    Article  ADS  Google Scholar 

  4. Folling, S. et al. Spatial quantum noise interferometry in expanding ultracold atom clouds. Nature 434, 481–484 (2005)

    Article  ADS  Google Scholar 

  5. Gerbier, F., Folling, 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 

  6. Kaganov, M. I. & Chubukov, A. V. Interacting magnons. Uspekhi Fizicheskikh Nauk. 153, 537–578 (1987)

    Article  Google Scholar 

  7. 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)

    Article  CAS  ADS  Google Scholar 

  8. 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 

  9. Capogrosso-Sansone, B., Prokof'ev, N. V. & Svistunov, B. V. Phase diagram and thermody-namics of the three-dimensional Bose-Hubbard model. Phys. Rev. B 75, 134302 (2007)

    Article  ADS  Google Scholar 

  10. Greiner, M., Mandel, O., Hansch, T. W. & Bloch, I. Collapse and revival of the matter wave field of a Bose-Einstein condensate. Nature 419, 51–54 (2002)

    Article  CAS  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  13. Hung, C. L., Zhang, X., Gemelke, N. & Chin, C. Accelerating evaporative cooling of atoms into Bose-Einstein condensation in optical traps. Phys. Rev. A 78, 011604 (2008)

    Article  ADS  Google Scholar 

  14. 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)

    Article  CAS  ADS  Google Scholar 

  15. Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Preprint at 〈〉 (2008)

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

    Article  CAS  ADS  Google Scholar 

  17. Ho, T. -L. & Zhou, Q. Obtaining phase diagram and thermodynamic quantities of bulk systems from the densities of trapped gases. Preprint at 〈〉 (2008)

  18. Tanatar, B., Minguzzi, A., Vignolo, P. & Tosi, M. P. Density profile of a Bose-Einstein condensate inside a pancake-shaped trap: observational consequences of the dimensional cross-over in the scattering properties. Phys. Lett. A 302, 131–136 (2002)

    Article  CAS  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Huang, K. Statistical Mechanics 152–154 (Wiley, 1963)

    Google Scholar 

  21. Esteve, J. et al. Observations of density fluctuations in an elongated Bose gas: ideal gas and quasicondensate regimes. Phys. Rev. Lett. 96, 090401 (2006)

    Article  Google Scholar 

Download references


We thank T. L. Ho, R. Scalettar, E. Mueller and R. Hulet for discussions. This work was supported by NSF (grant numbers PHY-0747907, NSF-MRSEC DMR-0213745) and ARO (grant number W911NF0710576) with funds from the DARPA OLE programme. N.G. acknowledges support from the Grainger Foundation.

Author Contributions All authors contributed to the analysis and writing of this manuscript; construction of the apparatus and acquisition of data was primarily the responsibility of C-L.H. and X.Z.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Cheng Chin.

Supplementary information

Supplementary Figure

This file contains Supplementary Figure 1 with its Legend. (PDF 131 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

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