Skip to main content

Thank you for visiting nature.com. 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.

  • Article
  • Published:

Probing superfluids in optical lattices by momentum-resolved Bragg spectroscopy

Nature Physics volume 6, pages 56–61 (2010)Cite this article

A Corrigendum to this article was published on 08 December 2009

This article has been updated

Abstract

The fundamental concept of superfluidity gives rise to fascinating effects and collective behaviour such as vortex creation and second sound. Using quantum gases in optical lattices, superfluids can be realized over a wide range of tunable parameters, with a continuous connection to the regime of strong correlation. However, for full experimental access and a comprehensive comparison with condensed-matter systems, there is a need for new detection techniques to probe their essential physics. Here we report on a comprehensive study of superfluids in optical lattices by Bragg spectroscopy. We present fully momentum-resolved measurements of the band structure and associated interaction effects at several lattice depths. In addition, we directly study the composition of excitations and observe strong indications for Bogoliubov backscattering. Our measurements demonstrate the applicability and limits of the Bogoliubov theory to describe excitation properties of superfluids in periodic potentials and should pave the way for detailed studies of strongly correlated phases.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: Experimental realization and schematic representation of the Bragg process in real and momentum space.
Figure 2: Excitation spectra.
Figure 3: Momentum composition of excitations.
Figure 4: Resonance spectra and corresponding band structure.
Figure 5: Shift of resonance position with density.
Figure 6: Resonance position versus atom number with respect to the excitation fraction.

Similar content being viewed by others

Change history

  • 08 December 2009

    In the version of this Article originally published, Fig. 4b was incorrect. This has been corrected in all versions of this Article.

References

  1. Stewart, J. T., Gaebler, J. P. & Jin, D. S. Using photoemission spectroscopy to probe a strongly interacting Fermi gas. Nature 454, 744–747 (2008).

    Article  ADS  Google Scholar 

  2. Kozuma, M. et al. Coherent splitting of Bose–Einstein condensed atoms with optically induced Bragg diffraction. Phys. Rev. Lett. 82, 871–875 (1999).

    Article  ADS  Google Scholar 

  3. Stenger, J. et al. Bragg spectroscopy of a Bose–Einstein condensate. Phys. Rev. Lett. 82, 4569–4573 (1999).

    Article  ADS  Google Scholar 

  4. Stamper-Kurn, D. M. et al. Excitations of phonons in a Bose–Einstein condensate by light scattering. Phys. Rev. Lett. 83, 2876–2879 (1999).

    Article  ADS  Google Scholar 

  5. Ozeri, R., Katz, N., Steinhauer, J. & Davidson, N. Colloquium: Bulk Bogoliubov excitations in a Bose–Einstein condensate. Rev. Mod. Phys. 77, 187–205 (2005).

    Article  ADS  Google Scholar 

  6. Papp, S. B. et al. Bragg spectroscopy of a strongly interacting 85Rb Bose–Einstein condensate. Phys. Rev. Lett. 101, 135301 (2008).

    Article  ADS  Google Scholar 

  7. Veeravalli, G., Kuhnle, E., Dyke, P. & Vale, C. J. Bragg spectroscopy of a strongly interacting Fermi gas. Phys. Rev. Lett. 101, 250403 (2008).

    Article  ADS  Google Scholar 

  8. 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  ADS  Google Scholar 

  9. 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 

  10. Schori, C., Stöferle, T., Moritz, H., Köhl, M. & Esslinger, T. Excitations of a superfluid in a three-dimensional optical lattice. Phys. Rev. Lett. 93, 240402 (2004).

    Article  ADS  Google Scholar 

  11. Du, X. et al. Bragg spectroscopy of a superfluid Bose–Hubbard gas. Preprint at <http://arxiv.org/abs/0704.2623> (2007).

  12. Fabbri, N. et al. Excitations of Bose–Einstein condensates in a one-dimensional periodic potential. Phys. Rev. A 79, 043623 (2009).

    Article  ADS  Google Scholar 

  13. Clément, D. et al. Exploring correlated 1D Bose gases from the superfluid to the Mott-insulator state by inelastic light scattering. Phys. Rev. Lett. 102, 155301 (2009).

    Article  ADS  Google Scholar 

  14. Menotti, C., Krämer, M., Pitaevskii, L. & Stringari, S. Dynamic structure factor of a Bose–Einstein condensate in a one-dimensional optical lattice. Phys. Rev. A 67, 053609 (2003).

    Article  ADS  Google Scholar 

  15. Roth, R. & Burnett, K. Dynamic structure factor of ultracold Bose and Fermi gases in optical lattices. J. Phys. B 37, 3893–3907 (2004).

    Article  ADS  Google Scholar 

  16. 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  ADS  Google Scholar 

  17. van Oosten, D., Dickerscheid, D. B. M., Farid, B., van der Straten, P. & Stoof, H. T. C. Inelastic light scattering from a Mott insulator. Phys. Rev. A 71, 021601 (2005).

    Article  ADS  Google Scholar 

  18. Rey, A. M., Blakie, P. B., Pupillo, G., Williams, C. J. & Clark, C. W. Bragg spectroscopy of ultracold atoms loaded in an optical lattice. Phys. Rev. A 72, 023407 (2005).

    Article  ADS  Google Scholar 

  19. Pupillo, G., Rey, A. M. & Batrouni, G. G. Bragg spectroscopy of trapped one-dimensional strongly interacting bosons in optical lattices: Probing the cake structure. Phys. Rev. A 74, 013601 (2006).

    Article  ADS  Google Scholar 

  20. Mathey, L., Danshita, I. & Clark, C. W. Creating a supersolid in one-dimensional Bose mixtures. Phys. Rev. A 79, 011602 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. 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  ADS  Google Scholar 

  23. Berg-Sørensen, K. & Mølmer, K. Bose–Einstein condensates in spatially periodic potentials. Phys. Rev. A 58, 1480–1484 (1998).

    Article  ADS  Google Scholar 

  24. Taylor, E. & Zaremba, E. Bogoliubov sound speed in periodically modulated Bose–Einstein condensates. Phys. Rev. A 68, 053611 (2003).

    Article  ADS  Google Scholar 

  25. Krämer, M., Menotti, C., Pitaevskii, L. & Stringari, S. Bose–Einstein condensates in 1D optical lattices: Compressibility, Bloch bands and elementary excitations. Eur. Phys. J. D 27, 247–261 (2003).

    Article  ADS  Google Scholar 

  26. Menotti, C., Krämer, M., Smerzi, A., Pitaevskii, L. & Stringari, S. Propagation of sound in a Bose–Einstein condensate in an optical lattice. Phys. Rev. A 70, 023609 (2004).

    Article  ADS  Google Scholar 

  27. Martikainen, J.-P. & Stoof, H. T. C. Longitudinal sound mode of a Bose–Einstein condensate in an optical lattice. Phys. Rev. A 69, 023608 (2004).

    Article  ADS  Google Scholar 

  28. Liang, Z. X., Dong, X., Zhang, Z. D. & Wu, B. Simple sound speed of a Bose–Einstein condensate in an optical lattice. Phys. Rev. A 78, 023622 (2008).

    Article  ADS  Google Scholar 

  29. van Oosten, D., van der Straten, P. & Stoof, H. T. C. Quantum phases in an optical lattice. Phys. Rev. A 63, 053601 (2001).

    Article  ADS  Google Scholar 

  30. Burnett, K., Edwards, M., Clark, C. W. & Shotter, M. The Bogoliubov approach to number squeezing of atoms in an optical lattice. J. Phys. B 35, 1671–1678 (2002).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. Dahan, M. B., Peik, E., Reichel, J., Castin, Y. & Salomon, C. Bloch oscillations of atoms in an optical potential. Phys. Rev. Lett. 76, 4508–4511 (1996).

    Article  ADS  Google Scholar 

  33. Vogels, J. M., Xu, K., Raman, C., Abo-Shaeer, J. R. & Ketterle, W. Experimental observation of the Bogoliubov transformation for a Bose–Einstein condensed gas. Phys. Rev. Lett. 88, 060402 (2002).

    Article  ADS  Google Scholar 

  34. Pitaevskii, L. & Stringari, S. Bose–Einstein Condensation (Oxford Univ. Press, 2003).

    MATH  Google Scholar 

  35. Müller, T., Fölling, S., Widera, A. & Bloch, I. State preparation and dynamics of ultracold atoms in higher lattice orbitals. Phys. Rev. Lett. 99, 200405 (2007).

    Article  ADS  Google Scholar 

  36. Dao, T.-L., Georges, A., Dalibard, J., Salomon, C. & Carusotto, I. Measuring the one-particle excitations of ultracold fermionic atoms by stimulated Raman spectroscopy. Phys. Rev. Lett. 98, 240402 (2008).

    Article  Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge valuable discussions with C. Becker, J. Heinze, U. Bissbort, W. Hofstetter, K. Rachor and K. Bongs. We also thank the Deutsche Forschungsgemeinschaft DFG for financial support within the Forschergruppe FOR801.

Author information

Authors and Affiliations

  1. Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany

    Philipp T. Ernst, Sören Götze, Jasper S. Krauser, Karsten Pyka & Klaus Sengstock

  2. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany

    Dirk-Sören Lühmann & Daniela Pfannkuche

Authors
  1. Philipp T. Ernst
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sören Götze
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jasper S. Krauser
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Karsten Pyka
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Dirk-Sören Lühmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Daniela Pfannkuche
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Klaus Sengstock
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

P.T.E. and S.G. carried out the experiments. J.S.K. and K.P. assisted in measurements. D.-S.L. and D.P. carried out the numerical calculations and discussed the theoretical implications. K.S. supervised the experiments. All authors contributed substantially to the discussion of the data and results and to the final manuscript by revisions and editing.

Corresponding author

Correspondence to Klaus Sengstock.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ernst, P., Götze, S., Krauser, J. et al. Probing superfluids in optical lattices by momentum-resolved Bragg spectroscopy. Nature Phys 6, 56–61 (2010). https://doi.org/10.1038/nphys1476

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys1476

This article is cited by

Search

Advanced search

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