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.

A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates


Supersolidity combines superfluid flow with long-range spatial periodicity of solids1, two properties that are often mutually exclusive. The original discussion of quantum crystals2 and supersolidity focused on solid 4He and triggered extensive experimental efforts3,4 that, instead of supersolidity, revealed exotic phenomena including quantum plasticity and mass supertransport4. The concept of supersolidity was then generalized from quantum crystals to other superfluid systems that break continuous translational symmetry. Bose–Einstein condensates with spin–orbit coupling are predicted to possess a stripe phase5,6,7 with supersolid properties8,9. Despite several recent studies of the miscibility of the spin components of such a condensate10,11,12, the presence of stripes has not been detected. Here we observe the predicted density modulation of this stripe phase using Bragg reflection (which provides evidence for spontaneous long-range order in one direction) while maintaining a sharp momentum distribution (the hallmark of superfluid Bose–Einstein condensates). Our work thus establishes a system with continuous symmetry-breaking properties, associated collective excitations and superfluid behaviour.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Origin of supersolid stripes and detection via Bragg scattering.
Figure 2: Density modulations from Raman beams, and quantitative studies of the supersolid stripes.
Figure 3: Phase diagram for spin–orbit-coupled BECs, and effect of Raman detuning on the supersolid stripes.
Figure 4: Bragg detection of a lattice supersolid caused by an antiferromagnetic spin texture.


  1. Boninsegni, M. & Prokof’ev, N. V. Supersolids: what and where are they? Rev. Mod. Phys. 84, 759–776 (2012)

    Article  ADS  CAS  Google Scholar 

  2. Chester, G. V. Speculations on Bose–Einstein condensation and quantum crystals. Phys. Rev. A 2, 256–258 (1970)

    Article  ADS  Google Scholar 

  3. Kim, E. & Chan, M. H. W. Probable observation of a supersolid helium phase. Nature 427, 225–227 (2004)

    Article  ADS  CAS  Google Scholar 

  4. Kuklov, A. B., Pollet, L., Prokof’ev, N. V. & Svistunov, B. V. Quantum plasticity and supersolid response in helium-4. Phys. Rev. B 90, 184508 (2014)

    Article  ADS  Google Scholar 

  5. Li, Y., Pitaevskii, L. P. & Stringari, S. Quantum tricriticality and phase transitions in spin-orbit-coupled Bose–Einstein condensates. Phys. Rev. Lett. 108, 225301 (2012)

    Article  ADS  Google Scholar 

  6. Ho, T.-L. & Zhang, S. Bose–Einstein condensates with spin-orbit interaction. Phys. Rev. Lett. 107, 150403 (2011)

    Article  ADS  Google Scholar 

  7. Wang, C., Gao, C., Jian, C.-M. & Zhai, H. Spin-orbit coupled spinor Bose–Einstein condensates. Phys. Rev. Lett. 105, 160403 (2010)

    Article  ADS  Google Scholar 

  8. Han, W., Juzeliu¯nas, G., Zhang, W. & Liu, W.-M. Supersolid with nontrivial topological spin textures in spin-orbit-coupled Bose gases. Phys. Rev. A 91, 013607 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  9. Li, Y., Martone, G. I., Pitaevskii, L. P. & Stringari, S. Superstripes and the excitation spectrum of a spin-orbit-coupled Bose–Einstein condensate. Phys. Rev. Lett. 110, 235302 (2013)

    Article  ADS  Google Scholar 

  10. Lin, Y.-J., Jiménez-García, K. & Spielman, I. B. Spin–orbit-coupled Bose–Einstein condensates. Nature 471, 83–86 (2011)

    Article  ADS  CAS  Google Scholar 

  11. Ji, S.-C. et al. Softening of roton and phonon modes in a Bose–Einstein condensate with spin-orbit coupling. Phys. Rev. Lett. 114, 105301 (2015)

    Article  ADS  Google Scholar 

  12. Ji, S.-C. et al. Experimental determination of the finite-temperature phase diagram of a spin–orbit coupled Bose gas. Nat. Phys. 10, 314–320 (2014)

    Article  CAS  Google Scholar 

  13. Giovanazzi, S., O’Dell, D. & Kurizki, G. Density modulations of Bose–Einstein condensates via laser-induced interactions. Phys. Rev. Lett. 88, 130402 (2002)

    Article  ADS  CAS  Google Scholar 

  14. Henkel, N., Nath, R. & Pohl, T. Three-dimensional roton excitations and supersolid formation in Rydberg-excited Bose–Einstein condensates. Phys. Rev. Lett. 104, 195302 (2010)

    Article  ADS  CAS  Google Scholar 

  15. Ostermann, S., Piazza, F. & Ritsch, H. Spontaneous crystallization of light and ultracold atoms. Phys. Rev. X 6, 021026 (2016)

    Google Scholar 

  16. Wessel, S. & Troyer, M. Supersolid hard-core bosons on the triangular lattice. Phys. Rev. Lett. 95, 127205 (2005)

    Article  ADS  Google Scholar 

  17. Léonard, J. et al. Supersolid formation in a quantum gas breaking a continuous translational symmetry. Nature (2017)

  18. Bulgac, A. & Forbes, M. M. Unitary Fermi supersolid: the Larkin–Ovchinnikov phase. Phys. Rev. Lett. 101, 215301 (2008)

    Article  ADS  Google Scholar 

  19. Chen, Y., Ye, J. & Tian, G. Classification of a supersolid: trial wavefunctions, symmetry breaking and excitation spectra. J. Low Temp. Phys. 169, 149–168 (2012)

    Article  ADS  CAS  Google Scholar 

  20. Stanescu, T. D., Anderson, B. & Galitski, V. Spin-orbit coupled Bose–Einstein condensates. Phys. Rev. A 78, 023616 (2008)

    Article  ADS  Google Scholar 

  21. Miyake, H. et al. Bragg scattering as a probe of atomic wave functions and quantum phase transitions in optical lattices. Phys. Rev. Lett. 107, 175302 (2011)

    Article  ADS  Google Scholar 

  22. Martone, G. I. Visibility and stability of superstripes in a spin-orbit-coupled Bose–Einstein condensate. Eur. Phys. J. Spec. Top. 224, 553–563 (2015)

    Article  CAS  Google Scholar 

  23. Burdick, N. Q., Tang, Y. & Lev, B. Long-lived spin-orbit-coupled degenerate dipolar Fermi gas. Phys. Rev. X 6, 031022 (2016)

    Google Scholar 

  24. Cheuk, L. W. et al. Spin-injection spectroscopy of a spin-orbit coupled Fermi gas. Phys. Rev. Lett. 109, 095302 (2012)

    Article  ADS  Google Scholar 

  25. Wang, P. et al. Spin-orbit coupled degenerate Fermi gases. Phys. Rev. Lett. 109, 095301 (2012)

    Article  ADS  Google Scholar 

  26. Song, B. et al. Spin-orbit coupled two-electron Fermi gases of ytterbium atoms. Phys. Rev. A 94, 061604(R) (2016)

    Article  ADS  Google Scholar 

  27. Li, J. et al. Spin-orbit coupling and spin textures in optical superlattices. Phys. Rev. Lett. 117, 185301 (2016)

    Article  ADS  Google Scholar 

  28. Baumann, K., Guerlin, C., Brennecke, F. & Esslinger, T. Dicke quantum phase transition with a superfluid gas in an optical cavity. Nature 464, 1301–1306 (2010)

    Article  ADS  CAS  Google Scholar 

  29. Sun, Q., Wen, L., Liu, W.-M., Juzeliu¯nas, G. & Ji, A.-C. Tunneling-assisted spin-orbit coupling in bilayer Bose–Einstein condensates. Phys. Rev. A 91, 033619 (2015)

    Article  ADS  Google Scholar 

  30. Zhai, H. Degenerate quantum gases with spin–orbit coupling. Rep. Prog. Phys. 78, 026001 (2015)

    Article  ADS  MathSciNet  Google Scholar 

Download references


We thank S. Stringari for discussions and W. C. Burton for reading the manuscript. We acknowledge support from the NSF through the Center for Ultracold Atoms and from award 1506369, from ARO-MURI Non-equilibrium Many-body Dynamics (grant W911NF-14-1-0003) and from AFOSR-MURI Quantum Phases of Matter (grant FA9550-14-1- 0035).

Author information

Authors and Affiliations



J.-R.L., W.H., J.L., B.S., S.B., F.C.T. and A.O.J. contributed to the building of the experiment. J.-R.L. led the experimental efforts. J.L. led the data analysis and simulations. W.H., J.-R.L. and W.K. conceived the experiment. All authors contributed to the writing of the manuscript.

Corresponding author

Correspondence to Jun-Ru Li.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks K. Hazzard and the other anonymous reviewer(s) for their contribution to the peer review of this work.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, JR., Lee, J., Huang, W. et al. A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates. Nature 543, 91–94 (2017).

Download citation

  • Received:

  • Accepted:

  • Published:

  • 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