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.

Direct observation of second-order atom tunnelling


Tunnelling of material particles through a classically impenetrable barrier constitutes one of the hallmark effects of quantum physics. When interactions between the particles compete with their mobility through a tunnel junction, intriguing dynamical behaviour can arise because the particles do not tunnel independently. In single-electron or Bloch transistors, for example, the tunnelling of an electron or Cooper pair can be enabled or suppressed by the presence of a second charge carrier due to Coulomb blockade1,2. Here we report direct, time-resolved observations of the correlated tunnelling of two interacting ultracold atoms through a barrier in a double-well potential. For the regime in which the interactions between the atoms are weak and tunnel coupling dominates, individual atoms can tunnel independently, similar to the case of a normal Josephson junction. However, when strong repulsive interactions are present, two atoms located on one side of the barrier cannot separate3, but are observed to tunnel together as a pair in a second-order co-tunnelling process. By recording both the atom position and phase coherence over time, we fully characterize the tunnelling process for a single atom as well as the correlated dynamics of a pair of atoms for weak and strong interactions. In addition, we identify a conditional tunnelling regime in which a single atom can only tunnel in the presence of a second particle, acting as a single atom switch. Such second-order tunnelling events, which are the dominating dynamical effect in the strongly interacting regime, have not been previously observed with ultracold atoms. Similar second-order processes form the basis of superexchange interactions between atoms on neighbouring lattice sites of a periodic potential, a central component of proposals for realizing quantum magnetism4,5,6,7.

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: Schematics of double-well generation, loading and detection sequences.
Figure 2: Tunnelling dynamics.
Figure 3: Tunnelling frequencies versus short-lattice depth (barrier height).
Figure 4: Conditional tunnelling.


  1. Averin, D. V. & Likharev, K. K. Coulomb blockade of single-electron tunneling, and coherent oscillations in small tunnel junctions. J. Low-Temp. Phys. 62, 345–373 (1986)

    Article  ADS  Google Scholar 

  2. Kouwenhoven, L. P. et al. in Mesoscopic Electron Transport (eds Sohn, L. L., Kouwenhoven, L. P. & Schön, G.) 105–214 (Kluwer, Dordrecht, 1997)

    Book  Google Scholar 

  3. Winkler, K. et al. Repulsively bound atom pairs in an optical lattice. Nature 441, 853–856 (2006)

    Article  ADS  CAS  Google Scholar 

  4. Auerbach, A. Interacting Electrons and Quantum Magnetism (Springer, Berlin, 1998)

    Google Scholar 

  5. Duan, L.-M., Demler, E. & Lukin, M. Controlling spin exchange interactions of ultracold atoms in an optical lattice. Phys. Rev. Lett. 91, 090402 (2003)

    Article  ADS  Google Scholar 

  6. Kuklov, A. & Svistunov, B. Counterflow superfluidity of two-species ultracold atoms in a commensurate optical lattice. Phys. Rev. Lett. 90, 100401 (2003)

    Article  ADS  CAS  Google Scholar 

  7. Altman, E., Hofstetter, W., Demler, E. & Lukin, M. Phase diagram of two-component bosons on an optical lattice. New J. Phys. 5, 113.1–113.19 (2003)

    Article  Google Scholar 

  8. Josephson, B. D. Possible new effects in superconductive tunnelling. Phys. Lett. 1, 251–253 (1962)

    Article  ADS  Google Scholar 

  9. Likharev, K. K. Superconducting weak links. Rev. Mod. Phys. 51, 101–159 (1979)

    Article  ADS  Google Scholar 

  10. Albiez, M. et al. Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. Phys. Rev. Lett. 95, 010402 (2005)

    Article  ADS  Google Scholar 

  11. Averin, D. V. Quantum computing and quantum measurement with mesoscopic Josephson junctions. Fortschr. Phys. 48, 1055–1074 (2000)

    Article  Google Scholar 

  12. Makhlin, Y., Schön, G. & Shnirman, A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys. 73, 357–400 (2001)

    Article  ADS  Google Scholar 

  13. De Franceschi, S. et al. Electron cotunneling in a semiconductor quantum dot. Phys. Rev. Lett. 86, 878–881 (2001)

    Article  ADS  CAS  Google Scholar 

  14. Zumbühl, D. M., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Cotunneling spectroscopy in few-electron quantum dots. Phys. Rev. Lett. 93, 256801–256804 (2004)

    Article  ADS  Google Scholar 

  15. 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  ADS  CAS  Google Scholar 

  16. 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  CAS  Google Scholar 

  17. 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  CAS  Google Scholar 

  18. 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  ADS  CAS  Google Scholar 

  19. 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 

  20. Anderlini, M., Sebby-Strabley, J., Kruse, J., Porto, J. V. & Phillips, W. D. Controlled atom dynamics in a double-well optical lattice. J. Phys. B 39, S199–S210 (2006)

    Article  ADS  CAS  Google Scholar 

  21. Sebby-Strabley, J. et al. Preparing and probing atomic number states with an atom interferometer. Phys. Rev. Lett. 98, 200405 (2007)

    Article  ADS  CAS  Google Scholar 

  22. Widera, A. et al. Coherent collisional spin dynamics in optical lattices. Phys. Rev. Lett. 95, 190405 (2005)

    Article  ADS  Google Scholar 

  23. Roos, C. F. et al. Bell states of atoms with ultralong lifetimes and their tomographic state analysis. Phys. Rev. Lett. 92, 220402 (2004)

    Article  ADS  CAS  Google Scholar 

  24. Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001)

    Article  ADS  CAS  Google Scholar 

  25. Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987)

    Article  ADS  CAS  Google Scholar 

  26. Trebst, S., Schollwöck, U., Troyer, M. & Zoller, P. d-Wave resonating valence bond states of fermionic atoms in optical lattices. Phys. Rev. Lett. 96, 250402–250404 (2006)

    Article  ADS  Google Scholar 

  27. Myatt, C. J., Burt, E. A., Ghrist, R. W., Cornell, E. A. & Wiemann, C. E. Production of two overlapping Bose-Einstein condensates by sympathetic cooling. Phys. Rev. Lett. 78, 586–589 (1997)

    Article  ADS  CAS  Google Scholar 

  28. Schmaljohann, H. et al. Dynamics of F = 2 spinor Bose-Einstein condensates. Phys. Rev. Lett. 92, 040402 (2004)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  30. Greiner, M., Bloch, I., Mandel, O., Hänsch, T. W. & Esslinger, T. Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Phys. Rev. Lett. 87, 160405 (2001)

    Article  ADS  CAS  Google Scholar 

Download references


We thank A. M. Rey and B. Paredes for discussions. We acknowledge funding through the DFG and the European Union (MC-EXT QUASICOMBS). R.S. acknowledges support by the EU QUDEDIS programme as well as SJCKMS and the Kempe I and II foundations.

Author information

Authors and Affiliations


Corresponding author

Correspondence to I. Bloch.

Ethics declarations

Competing interests

Reprints and permissions information is available at The authors declare no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Fölling, S., Trotzky, S., Cheinet, P. et al. Direct observation of second-order atom tunnelling. Nature 448, 1029–1032 (2007).

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