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:

Observation of Bose–Einstein condensation in a strong synthetic magnetic field

Nature Physics volume 11, pages 859–864 (2015)Cite this article

Subjects

Abstract

Extensions of Berry’s phase and the quantum Hall effect have led to the discovery of new states of matter with topological properties. Traditionally, this has been achieved using magnetic fields or spin–orbit interactions, which couple only to charged particles. For neutral ultracold atoms, synthetic magnetic fields have been created that are strong enough to realize the Harper–Hofstadter model. We report the first observation of Bose–Einstein condensation in this system and study the Harper–Hofstadter Hamiltonian with one-half flux quantum per lattice unit cell. The diffraction pattern of the superfluid state directly shows the momentum distribution of the wavefunction, which is gauge-dependent. It reveals both the reduced symmetry of the vector potential and the twofold degeneracy of the ground state. We explore an adiabatic many-body state preparation protocol via the Mott insulating phase and observe the superfluid ground state in a three-dimensional lattice with strong interactions.

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: Observation of Bose–Einstein condensation in the Harper–Hofstadter model.
Figure 2: Population imbalance of the two ground states of the HH Hamiltonian with 1/2 flux.
Figure 3: Decay of Bose–Einstein condensates in modulated lattices.
Figure 4: Experimental sequences for two different state preparation protocols.
Figure 5: HH model with strong interactions.

Similar content being viewed by others

References

  1. Chen, X., Gu, Z.-C., Liu, Z.-X. & Wen, X.-G. Symmetry-protected topological orders in interacting bosonic systems. Science 338, 1604–1606 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  2. Wang, C., Potter, A. C. & Senthil, T. Classification of interacting electronic topological insulators in three dimensions. Science 343, 629–631 (2014).

    Article  ADS  Google Scholar 

  3. Willett, R. et al. Observation of an even-denominator quantum number in the fractional quantum Hall effect. Phys. Rev. Lett. 59, 1776–1779 (1987).

    Article  ADS  Google Scholar 

  4. Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

    Article  ADS  Google Scholar 

  5. Deng, M. T. et al. Anomalous zero-bias conductance peak in a Nb–InSb nanowire–Nb hybrid device. Nano Lett. 12, 6414–6419 (2012).

    Article  ADS  Google Scholar 

  6. Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346, 602–607 (2014).

    Article  ADS  Google Scholar 

  7. Madison, K. W., Chevy, F., Wohlleben, W. & Dalibard, J. Vortex formation in a stirred Bose–Einstein condensate. Phys. Rev. Lett. 84, 806–809 (2000).

    Article  ADS  Google Scholar 

  8. Abo-Shaeer, J., Raman, C., Vogels, J. & Ketterle, W. Observation of vortex lattices in Bose–Einstein condensates. Science 292, 476–479 (2001).

    Article  ADS  Google Scholar 

  9. Gemelke, N., Sarajlic, E. & Chu, S. Rotating few-body atomic systems in the fractional quantum Hall regime. Preprint at http://arXiv.org/abs/1007.2677 (2010).

  10. Jaksch, D. & Zoller, P. Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms. New J. Phys. 5, 56 (2003).

    Article  ADS  Google Scholar 

  11. Kolovsky, A. R. Creating artificial magnetic fields for cold atoms by photon-assisted tunneling. Europhys. Lett. 93, 20003 (2011).

    Article  ADS  Google Scholar 

  12. Lin, Y.-J., Compton, R. L., Jimenez-Garcia, K., Porto, J. V. & Spielman, I. B. Synthetic magnetic fields for ultracold neutral atoms. Nature 462, 628–632 (2009).

    Article  ADS  Google Scholar 

  13. Aidelsburger, M. et al. Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. Phys. Rev. Lett. 111, 185301 (2013).

    Article  ADS  Google Scholar 

  14. Miyake, H., Siviloglou, G. A., Kennedy, C. J., Burton, W. C. & Ketterle, W. Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices. Phys. Rev. Lett. 111, 185302 (2013).

    Article  ADS  Google Scholar 

  15. Struck, J. et al. Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields. Nature Phys. 9, 738–743 (2013).

    Article  ADS  Google Scholar 

  16. Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014).

    Article  ADS  Google Scholar 

  17. Harper, P. G. Single band motion of conduction electrons in a uniform magnetic field. Proc. Phys. Soc. A 68, 874–878 (1955).

    Article  ADS  Google Scholar 

  18. Azbel, M. Y. Energy spectrum of a conduction electron in a magnetic field. Sov. Phys. JETP 19, 634–645 (1964).

    Google Scholar 

  19. Hofstadter, D. R. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev. B 14, 2239–2249 (1976).

    Article  ADS  Google Scholar 

  20. Aidelsburger, M. et al. Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nature Phys. 11, 162–166 (2015).

    Article  ADS  Google Scholar 

  21. Goldman, N., Dalibard, J., Aidelsburger, M. & Cooper, N. R. Periodically driven quantum matter: The case of resonant modulations. Phys. Rev. A 91, 033632 (2015).

    Article  ADS  Google Scholar 

  22. Bukov, M. & Polkovnikov, A. Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper–Hofstadter Hamiltonian. Phys. Rev. A 90, 043613 (2014).

    Article  ADS  Google Scholar 

  23. Bilitewski, T. & Cooper, N. R. Scattering theory for Floquet–Bloch states. Phys. Rev. A 91, 033601 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  24. Choudhury, S. & Mueller, E. J. Transverse collisional instabilities of a Bose–Einstein condensate in a driven one-dimensional lattice. Phys. Rev. A 91, 023624 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  25. Aidelsburger, M. et al. Experimental realization of strong effective magnetic fields in an optical lattice. Phys. Rev. Lett. 107, 255301 (2011).

    Article  ADS  Google Scholar 

  26. Atala, M. et al. Observation of chiral currents with ultracold atoms in bosonic ladders. Nature Phys. 10, 588–593 (2014).

    Article  ADS  Google Scholar 

  27. Stuhl, B. K., Lu, H.-I., Aycock, L. M., Genkina, D. & Spielman, I. B. Visualizing edge states with an atomic Bose gas in the quantum Hall regime. Preprint at http://arXiv.org/abs/1502.02496 (2015).

  28. Lim, L.-K., Hemmerich, A. & Smith, C. M. Artificial staggered magnetic field for ultracold atoms in optical lattices. Phys. Rev. A 81, 023404 (2010).

    Article  ADS  Google Scholar 

  29. Möller, G. & Cooper, N. R. Condensed ground states of frustrated Bose–Hubbard models. Phys. Rev. A 82, 063625 (2010).

    Article  ADS  Google Scholar 

  30. Powell, S., Barnett, R., Sensarma, R. & Das Sarma, S. Bogoliubov theory of interacting bosons on a lattice in a synthetic magnetic field. Phys. Rev. A 83, 013612 (2011).

    Article  ADS  Google Scholar 

  31. Polini, M., Fazio, R., MacDonald, A. H. & Tosi, M. P. Realization of fully frustrated Josephson-junction arrays with cold atoms. Phys. Rev. Lett. 95, 010401 (2005).

    Article  ADS  Google Scholar 

  32. Kohmoto, M. Topological invariant and the quantization of the Hall conductance. Ann. Phys. 160, 343–354 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  33. Lin, Y.-J. et al. A synthetic electric force acting on neutral atoms. Nature Phys. 7, 531–534 (2011).

    Article  ADS  Google Scholar 

  34. Polak, T. P. & Zaleski, T. A. Time-of-flight patterns of ultracold bosons in optical lattices in various Abelian artificial magnetic field gauges. Phys. Rev. A 87, 033614 (2013).

    Article  ADS  Google Scholar 

  35. Ozawa, T., Price, H. M. & Carusotto, I. The momentum-space Harper–Hofstadter model. Preprint at http://arXiv.org/abs/1411.1203 (2014).

  36. Parker, C. V., Ha, L.-C. & Chin, C. Direct observation of effective ferromagnetic domains of cold atoms in a shaken optical lattice. Nature Phys. 9, 769–774 (2013).

    Article  ADS  Google Scholar 

  37. Haller, E. et al. Inducing transport in a dissipation-free lattice with super Bloch oscillations. Phys. Rev. Lett. 104, 200403 (2010).

    Article  ADS  Google Scholar 

  38. Alberti, A., Ferrari, G., Ivanov, V., Chiofalo, M. & Tino, G. Atomic wave packets in amplitude-modulated vertical optical lattices. New J. Phys. 12, 065037 (2010).

    Article  ADS  Google Scholar 

  39. Braun, S. et al. Negative absolute temperature for motional degrees of freedom. Science 339, 52–55 (2013).

    Article  ADS  Google Scholar 

  40. Zurek, W. H., Dorner, U. & Zoller, P. Dynamics of a quantum phase transition. Phys. Rev. Lett. 95, 105701 (2005).

    Article  ADS  Google Scholar 

  41. Umucalılar, R. O. & Oktel, M. Ö. Phase boundary of the boson Mott insulator in a rotating optical lattice. Phys. Rev. A 76, 055601 (2007).

    Article  ADS  Google Scholar 

  42. Dubček, T. et al. Weyl points in three-dimensional optical lattices: Synthetic magnetic monopoles in momentum space. Phys. Rev. Lett. 114, 225301 (2015).

    Article  ADS  Google Scholar 

  43. Kennedy, C. J., Siviloglou, G. A., Miyake, H., Burton, W. C. & Ketterle, W. Spin–orbit coupling and quantum spin Hall effect for neutral atoms without spin flips. Phys. Rev. Lett. 111, 225301 (2013).

    Article  ADS  Google Scholar 

  44. Lewenstein, M., Sanpera, A. & Ahufinger, V. Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems (Oxford Univ. Press, 2012).

    Book  Google Scholar 

  45. Goldman, N., Juzeliūnas, G., Öhberg, P. & Spielman, I. B. Light-induced gauge fields for ultracold atoms. Rep. Prog. Phys. 77, 126401 (2014).

    Article  ADS  Google Scholar 

  46. Cooper, N. R. & Dalibard, J. Reaching fractional quantum Hall states with optical flux lattices. Phys. Rev. Lett. 110, 185301 (2013).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge Quantel Laser for their gracious support and use of an EYLSA laser for our main cooling and trapping light, G. Siviloglou and Y. Lensky for experimental contributions, and E. Mueller, S. Choudhury, A. Jamison, M. Lukin, S. D. Sarma, S. Parameswaran, E. Altman, E. Demler, N. Cooper and G. Möller for stimulating discussions. W.C.C. acknowledges support of the Samsung Scholarship. This work was supported by the NSF through grant PHY-0969731, through the Center for Ultracold Atoms, AFOSR MURI grant FA9550-14-1-0035 and ARO MURI grant no. W911NF-14-1-0003.

Author information

Authors and Affiliations

  1. Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    Colin J. Kennedy, William Cody Burton, Woo Chang Chung & Wolfgang Ketterle

Authors
  1. Colin J. Kennedy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William Cody Burton
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Woo Chang Chung
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wolfgang Ketterle
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to experimental work, data analysis and manuscript preparation.

Corresponding author

Correspondence to Colin J. Kennedy.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 413 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kennedy, C., Burton, W., Chung, W. et al. Observation of Bose–Einstein condensation in a strong synthetic magnetic field. Nature Phys 11, 859–864 (2015). https://doi.org/10.1038/nphys3421

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys3421

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