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Probing an ultracold-atom crystal with matter waves


Atomic quantum gases in optical lattices serve as a versatile testbed for important concepts of modern condensed-matter physics. The availability of methods to characterize strongly correlated phases is crucial for the study of these systems. Diffraction techniques to reveal long-range spatial structure, which may complement in situ detection methods, have been largely unexplored. Here we experimentally demonstrate that Bragg diffraction of neutral atoms can be used for this purpose. Using a one-dimensional Bose gas as a source of matter waves, we are able to infer the spatial ordering and on-site localization of atoms confined to an optical lattice. We also study the suppression of inelastic scattering between incident matter waves and the lattice-trapped atoms, occurring for increased lattice depth. Furthermore, we use atomic de Broglie waves to detect forced antiferromagnetic ordering in an atomic spin mixture, demonstrating the suitability of our method for the non-destructive detection of spin-ordered phases in strongly correlated atomic gases.

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Figure 1: Interspecies collisions of one-dimensional bosons.
Figure 2: Probe scattering from a crystalline target.
Figure 3: Detecting forced antiferromagnetic order by means of matter-wave scattering.


  1. Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Holt-Saunders International Editions, 1976).

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Kuklov, A. B. & Svistunov, B. V. Testing quantum correlations in a confined atomic cloud by the scattering of fast atoms. Phys. Rev. A 60, R769–R772 (1999).

    Article  ADS  Google Scholar 

  4. Sanders, S. N., Mintert, F. & Heller, E. J. Matter-wave scattering from ultracold atoms in an optical lattice. Phys. Rev. Lett. 105, 035301 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Altman, E., Demler, E. & Lukin, M. D. Probing many-body states of ultracold atoms via noise correlations. Phys. Rev. A 70, 013603 (2004).

    Article  ADS  Google Scholar 

  7. 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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Gericke, T., Würtz, P., Reitz, D., Langen, T. & Ott, H. High-resolution scanning electron microscopy of an ultracold quantum gas. Nature Phys. 4, 949–953 (2008).

    Article  ADS  Google Scholar 

  11. Javanainen, J. & Ruostekoski, J. Optical detection of fractional particle number in an atomic Fermi–Dirac Gas. Phys. Rev. Lett. 91, 150404 (2003).

    Article  ADS  Google Scholar 

  12. De Vega, I., Cirac, J. I. & Porras, D. Detection of spin correlations in optical lattices by light scattering. Phys. Rev. A 77, 051804 (2008).

    Article  ADS  Google Scholar 

  13. Corcovilos, T. A., Baur, S. K., Hitchcock, J. M., Mueller, E. J. & Hulet, R. G. Detecting antiferromagnetism of atoms in an optical lattice via optical Bragg scattering. Phys. Rev. A 81, 013415 (2010).

    Article  ADS  Google Scholar 

  14. Weitenberg, C. et al. Coherent light scattering from a two-dimensional Mott insulator. Phys. Rev. Lett. 106, 215301 (2011).

    Article  ADS  Google Scholar 

  15. Pino, J. M., Wild, R. J., Makotyn, P., Jin, D. S. & Cornell, E. A. Photon counting for Bragg spectroscopy of quantum gases. Phys. Rev. A 83, 033615 (2011).

    Article  ADS  Google Scholar 

  16. Olshanii, M. Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Phys. Rev. Lett. 81, 938–941 (1998).

    Article  ADS  Google Scholar 

  17. Kinoshita, T., Wenger, T. & Weiss, D. S. A quantum Newton’s cradle. Nature 440, 900–903 (2006).

    Article  ADS  Google Scholar 

  18. Soltan-Panahi, P. et al. Multi-component quantum gases in spin-dependent hexagonal lattices. Nature Phys. 7, 434–440 (2011).

    ADS  Google Scholar 

  19. Deutsch, I. H. & Jessen, P. S. Quantum-state control in optical lattices. Phys. Rev. A 57, 1972–1986 (1998).

    Article  ADS  Google Scholar 

  20. Pertot, D., Gadway, B. & Schneble, D. Collinear four-wave mixing of two-component matter waves. Phys. Rev. Lett. 104, 200402 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. 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 

  23. Palzer, S., Zipkes, C., Sias, C. & Köhl, M. Quantum transport through a Tonks–Girardeau gas. Phys. Rev. Lett. 103, 150601 (2009).

    Article  ADS  Google Scholar 

  24. McKay, D. & DeMarco, B. Thermometry with spin-dependent lattices. New J. Phys. 12, 055013 (2010).

    Article  ADS  Google Scholar 

  25. Clément, D., Fabbri, N., Fallani, L., Fort, C. & Inguscio, M. 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 

  26. Ernst, P. T. et al. Probing superfluids in optical lattices by momentum-resolved Bragg spectroscopy. Nature Phys. 6, 56–61 (2010).

    Article  ADS  Google Scholar 

  27. Roscilde, T. & Cirac, J. I. Quantum emulsion: A glassy phase of bosonic mixtures in optical lattices. Phys. Rev. Lett. 98, 190402 (2007).

    Article  ADS  Google Scholar 

  28. Gadway, B., Pertot, D., Reeves, J., Vogt, M. & Schneble, D. Glassy behavior in a binary atomic mixture. Phys. Rev. Lett. 107, 145306 (2011).

    Article  ADS  Google Scholar 

  29. Fabbri, N., Clément, D., Fallani, L., Fort, C. & Inguscio, M. Momentum-resolved study of an array of one-dimensional strongly phase-fluctuating Bose gases. Phys. Rev. A 83, 031604 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Madison, K. W., Chevy, F., Bretin, V. & Dalibard, J. Stationary states of a rotating Bose–Einstein condensate: Routes to vortex nucleation. Phys. Rev. Lett. 86, 4443–4446 (2001).

    Article  ADS  Google Scholar 

  32. Raman, C., Abo-Shaeer, J. R., Vogels, J. M., Xu, K. & Ketterle, W. Vortex nucleation in a stirred Bose–Einstein condensate. Phys. Rev. Lett. 87, 210402 (2001).

    Article  ADS  Google Scholar 

  33. Pupillo, G., Griessner, A., Micheli, A., Ortner, M., Wang, D-W. & Zoller, P. Cold atoms and molecules in self-assembled dipolar lattices. Phys. Rev. Lett. 100, 050402 (2008).

    Article  ADS  Google Scholar 

  34. Pertot, D., Greif, D., Albert, S., Gadway, B. & Schneble, D. Versatile transporter apparatus for experiments with optically trapped Bose–Einstein condensates. J. Phys. B 42, 215305 (2009).

    Article  ADS  Google Scholar 

  35. Girardeau, M. Relationship between systems of impenetrable bosons and fermions in one dimension. J. Math. Phys. 1, 516–523 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  36. Lieb, E. H. & Liniger, W. Exact analysis of an interacting Bose gas. I. The general solution and the ground state. Phys. Rev. 130, 1605–1616 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  37. Dunjko, V., Lorent, V. & Olshanii, M. Bosons in cigar-shaped traps: Thomas–Fermi regime, Tonks–Girardeau regime, and in between. Phys. Rev. Lett. 86, 5413–5416 (2001).

    Article  ADS  Google Scholar 

  38. Gadway, B., Pertot, D., Reimann, R., Cohen, M. G. & Schneble, D. Analysis of Kapitza–Dirac diffraction patterns beyond the Raman–Nath regime. Opt. Express 17, 19173–19180 (2009).

    Article  ADS  Google Scholar 

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We thank G. Pupillo and K. Le Hur for discussions, and M. G. Cohen and T. Bergeman for valuable comments on the manuscript. This work was supported by the National Science Foundation (NSF) (PHY-0855643), and the Research Foundation of The State University of New York (SUNY). B.G. and J.R. acknowledge support from the Graduate Assistance in Areas of National Need (GAANN) program of the US Department of Education.

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D.S., B.G. and D.P. conceived the experiment. B.G. and D.P. carried out the measurements, with assistance from J.R. B.G. performed the data analysis, with contributions by D.P. D.S. supervised the project. All authors discussed the results and implications. B.G. and D.S. wrote the manuscript with contributions from D.P.

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Correspondence to Dominik Schneble.

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The authors declare no competing financial interests.

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Gadway, B., Pertot, D., Reeves, J. et al. Probing an ultracold-atom crystal with matter waves. Nature Phys 8, 544–549 (2012).

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