Letter | Published:

Self-bound droplets of a dilute magnetic quantum liquid

Nature volume 539, pages 259262 (10 November 2016) | Download Citation


Self-bound many-body systems are formed through a balance of attractive and repulsive forces and occur in many physical scenarios. Liquid droplets are an example of a self-bound system, formed by a balance of the mutual attractive and repulsive forces that derive from different components of the inter-particle potential. It has been suggested1,2 that self-bound ensembles of ultracold atoms should exist for atom number densities that are 108 times lower than in a helium droplet, which is formed from a dense quantum liquid. However, such ensembles have been elusive up to now because they require forces other than the usual zero-range contact interaction, which is either attractive or repulsive but never both. On the basis of the recent finding that an unstable bosonic dipolar gas can be stabilized by a repulsive many-body term3, it was predicted that three-dimensional self-bound quantum droplets of magnetic atoms should exist4,5. Here we report the observation of such droplets in a trap-free levitation field. We find that this dilute magnetic quantum liquid requires a minimum, critical number of atoms, below which the liquid evaporates into an expanding gas as a result of the quantum pressure of the individual constituents. Consequently, around this critical atom number we observe an interaction-driven phase transition between a gas and a self-bound liquid in the quantum degenerate regime with ultracold atoms. These droplets are the dilute counterpart of strongly correlated self-bound systems such as atomic nuclei6 and helium droplets7.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    Quantum mechanical stabilization of a collapsing Bose–Bose mixture. Phys. Rev. Lett. 115, 155302 (2015)

  2. 2.

    Dilute quantum droplets. Phys. Rev. Lett. 89, 050402 (2002)

  3. 3.

    , , , & Observation of quantum droplets in a strongly dipolar Bose gas. Phys. Rev. Lett. 116, 215301 (2016)

  4. 4.

    & Ground-state properties and elementary excitations of quantum droplets in dipolar Bose–Einstein condensates. Phys. Rev. A 94, 043618 (2016)

  5. 5.

    , , & Self-bound dipolar droplet: a localized matter wave in free space. Phys. Rev. A 94, 021602(R) (2016)

  6. 6.

    , & Self-consistent mean-field models for nuclear structure. Rev. Mod. Phys. 75, 121–180 (2003)

  7. 7.

    & Helium nanodroplets and trapped Bose–Einstein condensates as prototypes of finite quantum fluids. J. Chem. Phys. 115, 10078–10089 (2001)

  8. 8.

    The Universe in a Helium Droplet 27–31 (Oxford Univ. Press, 2009)

  9. 9.

    & Superfluid helium droplets: a uniquely cold nanomatrix for molecules and molecular complexes. Angew. Chem. Int. Ed. 43, 2622–2648 (2004)

  10. 10.

    et al. Shapes and vorticities of superfluid helium nanodroplets. Science 345, 906–909 (2014)

  11. 11.

    et al. Observing the Rosensweig instability of a quantum ferrofluid. Nature 530, 194–197 (2016)

  12. 12.

    et al. Quantum-fluctuation-driven crossover from a dilute Bose–Einstein condensate to a macro-droplet in a dipolar quantum fluid. Preprint at (2016)

  13. 13.

    , , & Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225–1286 (2010)

  14. 14.

    , , , & s-wave scattering lengths of the strongly dipolar bosons 162Dy and 164Dy. Phys. Rev. A 92, 022703 (2015)

  15. 15.

    et al. Emergence of chaotic scattering in ultracold Er and Dy. Phys. Rev. X 5, 041029 (2015)

  16. 16.

    , , & Strongly dipolar Bose–Einstein condensate of dysprosium. Phys. Rev. Lett. 107, 190401 (2011)

  17. 17.

    , , , & The physics of dipolar bosonic quantum gases. Rep. Prog. Phys. 72, 126401 (2009)

  18. 18.

    , , & Ground-state phase diagram of a dipolar condensate with quantum fluctuations. Phys. Rev. A 94, 033619 (2016)

  19. 19.

    & Quantum filaments in dipolar Bose–Einstein condensates. Phys. Rev. A 93, 061603 (2016)

  20. 20.

    & Quantum fluctuations in dipolar Bose gases. Phys. Rev. A 84, 041604 (2011)

  21. 21.

    & Beyond mean-field low-lying excitations of dipolar Bose gases. Phys. Rev. A 86, 063609 (2012)

  22. 22.

    Carlo study on a droplet of a dipolar Bose–Einstein condensate stabilized by quantum fluctuation. J. Phys. Soc. Jpn 85, 053001 (2016)

Download references


We thank H. P. Büchler, L. Santos, F. Ferlaino, W. Ketterle, H. Sadeghpour, M. Zwierlein and V. Vuletic´ for discussions. This work is supported by the German Research Foundation (DFG) within SFB/TRR21 as well as FOR 2247. I.F.-B. acknowledges support from the EU within Horizon2020 Marie Skłodowska Curie IF (703419 DipInQuantum).

Author information


  1. 5. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

    • Matthias Schmitt
    • , Matthias Wenzel
    • , Fabian Böttcher
    • , Igor Ferrier-Barbut
    •  & Tilman Pfau


  1. Search for Matthias Schmitt in:

  2. Search for Matthias Wenzel in:

  3. Search for Fabian Böttcher in:

  4. Search for Igor Ferrier-Barbut in:

  5. Search for Tilman Pfau in:


All authors discussed the results, made critical contributions to the work and contributed to the writing of the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Matthias Schmitt or Tilman Pfau.

Reviewer Information Nature thanks B. Blakie, R. Hulet and the other anonymous reviewer(s) for their contribution to the peer review of this work.

About this article

Publication history






Further reading


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.