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.

Kibble–Zurek universality in a strongly interacting Fermi superfluid


The Kibble–Zurek mechanism describes the spontaneous formation of topological defects in a system crossing a continuous phase transition1,2. Its central premise is the notion of universality, which states that the characteristic scaling exponent describing the dependence of the defect density on the quench rate is determined by the underlying symmetries of the system. Whether this universality can be extended to strongly interacting systems, such as a unitary Fermi gas, is an open question that has recently drawn attention in the context of holographic theories3,4. Here, we report the observation of the Kibble–Zurek universality in a strongly interacting Fermi superfluid. As the microscopic nature of superfluidity is tuned from Bose–Einstein condensation of tightly bound molecules to Bardeen–Cooper–Schrieffer superfluidity of long-range fermion pairs, the thermal quench formation of vortices reveals a constant scaling exponent arising from the U(1) gauge symmetry of the system. In rapid quenches, destructive vortex collisions lead to the saturation of vortex densities, the values of which can be universally scaled by the interaction-dependent area of the vortex cores. This work paves the way for precision studies of non-equilibrium dynamics in a highly tunable, strongly correlated many-fermion system5,6.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Spontaneous defect formation during the normal-to-superfluid phase transition in a strongly interacting Fermi gas.
Fig. 2: Vortex number versus quench time.
Fig. 3: Kibble–Zurek exponents in the BEC–BCS crossover.
Fig. 4: Characterization of spontaneous vortex formation across the BEC–BCS crossover.

Data availability

The data supporting this manuscript are available from the corresponding authors on reasonable request.


  1. 1.

    Kibble, T. W. Topology of cosmic domains and strings. J. Phys. A 9, 1387–1398 (1976).

    Article  ADS  Google Scholar 

  2. 2.

    Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985).

    Article  ADS  Google Scholar 

  3. 3.

    Sonner, J., del Campo, A. & Zurek, W. H. Universal far-from-equilibrium dynamics of a holographic superconductor. Nat. Commun. 6, 8406 (2015).

    Article  Google Scholar 

  4. 4.

    Chesler, P. M., García-García, A. M. & Liu, H. Defect formation beyond Kibble-Zurek mechanism and holography. Phys. Rev. X 5, 021015 (2015).

    Google Scholar 

  5. 5.

    Bulgac, A., Luo, Y. L., Magierski, P., Roche, K. J. & Yu, Y. Real-time dynamics of quantized vortices in a unitary Fermi superfluid. Science 332, 1288–1291 (2011).

    Article  ADS  Google Scholar 

  6. 6.

    Adams, A., Carr, L. D., Schäfer, T., Steinberg, P. & Thomas, J. E. Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality. New J. Phys. 14, 115009 (2012).

    MathSciNet  Article  ADS  Google Scholar 

  7. 7.

    Hohenberg, P. C. & Halperin, B. I. Theory of dynamic critical phenomena. Rev. Mod. Phys. 49, 435–479 (1977).

    Article  ADS  Google Scholar 

  8. 8.

    Chuang, I., Durrer, R., Turok, N. & Yurke, B. Cosmology in the laboratory: defect dynamics in liquid crystals. Science 251, 1336–1342 (1991).

    Article  ADS  Google Scholar 

  9. 9.

    Hendry, P. C., Lawson, N. S., Lee, R. A. M., McClintock, P. V. E. & Williams, C. D. H. Generation of defects in superfluid 4He as an analogue of the formation of cosmic strings. Nature 368, 315–317 (1994).

    Article  ADS  Google Scholar 

  10. 10.

    Bäuerle, C., Bunkov, Y. M., Fisher, S. N., Godfrin, H. & Pickett, G. R. Laboratory simulation of cosmic string formation in the early Universe using superfluid 3He. Nature 382, 332–334 (1996).

    Article  ADS  Google Scholar 

  11. 11.

    Ruutu, V. M. H. et al. Vortex formation in neutron-irradiated superfluid 3He as an analogue of cosmological defect formation. Nature 382, 334–336 (1996).

    Article  ADS  Google Scholar 

  12. 12.

    Pyka, K. et al. Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals. Nat. Commun. 4, 2291 (2013).

    Article  ADS  Google Scholar 

  13. 13.

    Ulm, S. et al. Observation of the Kibble–Zurek scaling law for defect formation in ion crystals. Nat. Commun. 4, 2290 (2013).

    Article  ADS  Google Scholar 

  14. 14.

    Ejtemaee, S. & Haljan, P. C. Spontaneous nucleation and dynamics of kink defects in zigzag arrays of trapped ions. Phys. Rev. A 87, 051401 (2013).

    Article  ADS  Google Scholar 

  15. 15.

    Weiler, C. N. et al. Spontaneous vortices in the formation of Bose-Einstein condensates. Nature 455, 948–951 (2008).

    Article  ADS  Google Scholar 

  16. 16.

    Lamporesi, G., Donadello, S., Serafini, S., Dalfovo, F. & Ferrari, G. Spontaneous creation of Kibble-Zurek solitons in a Bose-Einstein condensate. Nat. Phys. 9, 656–660 (2013).

    Article  Google Scholar 

  17. 17.

    Corman, L. et al. Quench-induced supercurrents in an annular Bose gas. Phys. Rev. Lett. 113, 135302 (2014).

    Article  ADS  Google Scholar 

  18. 18.

    Navon, N., Gaunt, A. L., Smith, R. P. & Hadzibabic, Z. Critical dynamics of spontaneous symmetry breaking in a homogeneous Bose gas. Science 347, 167–170 (2015).

    Article  ADS  Google Scholar 

  19. 19.

    Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of ultracold atomic Fermi gases. Rev. Mod. Phys. 80, 1215–1274 (2008).

    Article  ADS  Google Scholar 

  20. 20.

    Zwerger, W. (ed.) Lecture Notes in Physics: The BCSBEC Crossover and the Unitary Fermi Gas Vol. 836 (Springer, 2011).

  21. 21.

    Nozières, P. & Schmitt-Rink, S. Bose condensation in an attractive fermion gas: from weak to strong coupling superconductivity. J. Low. Temp. Phys. 59, 195–211 (1985).

    Article  ADS  Google Scholar 

  22. 22.

    Regal, C. A., Greiner, M. & Jin, D. S. Observation of resonance condensation of fermionic atom pairs. Phys. Rev. Lett. 92, 040403 (2004).

    Article  ADS  Google Scholar 

  23. 23.

    Chen, Q., Regal, C. A., Greiner, M., Jin, D. S. & Levin, K. Understanding the superfluid phase diagram in trapped Fermi gases. Phys. Rev. A 73, 041601 (2006).

    Article  ADS  Google Scholar 

  24. 24.

    Miller, D. E. et al. Critical velocity for superfluid flow across the BEC-BCS crossover. Phys. Rev. Lett. 99, 070402 (2007).

    Article  ADS  Google Scholar 

  25. 25.

    Weimer, W. et al. Critical velocity in the BEC-BCS crossover. Phys. Rev. Lett. 114, 095301 (2015).

    Article  ADS  Google Scholar 

  26. 26.

    Park, J. W., Ko, B. & Shin, Y. Critical vortex shedding in a strongly interacting fermionic superfluid. Phys. Rev. Lett. 121, 225301 (2018).

    Article  ADS  Google Scholar 

  27. 27.

    Heiselberg, H. Fermi systems with long scattering lengths. Phys. Rev. A 63, 043606 (2001).

    Article  ADS  Google Scholar 

  28. 28.

    del Campo, A., Retzker, A. & Plenio, M. B. The inhomogeneous Kibble–Zurek mechanism: vortex nucleation during Bose–Einstein condensation. New J. Phys. 13, 083022 (2011).

    Article  Google Scholar 

  29. 29.

    Donadello, S. et al. Creation and counting of defects in a temperature-quenched Bose-Einstein condensate. Phys. Rev. A 94, 023628 (2016).

    Article  ADS  Google Scholar 

  30. 30.

    Liu, I. K. et al. Dynamical equilibration across a quenched phase transition in a trapped quantum gas. Comm. Phys. 1, 24 (2018).

    Article  ADS  Google Scholar 

  31. 31.

    Donner, T. et al. Critical behavior of a trapped interacting Bose gas. Science 315, 1556–1558 (2007).

    Article  ADS  Google Scholar 

  32. 32.

    Taylor, E. Critical behavior in trapped strongly interacting Fermi gases. Phys. Rev. A 80, 023612 (2009).

    Article  ADS  Google Scholar 

  33. 33.

    Debelhoir, T. & Dupuis, N. Critical region of the superfluid transition in the BCS-BEC crossover. Phys. Rev. A 93, 023642 (2016).

    Article  ADS  Google Scholar 

  34. 34.

    Gehm, M. E., Hemmer, S. L., O’Hara, K. M. & Thomas, J. E. Unitarity-limited elastic collision rate in a harmonically trapped Fermi gas. Phys. Rev. A 68, 011603 (2003).

    Article  ADS  Google Scholar 

  35. 35.

    Jelić, A. & Cugliandolo, L. F. Quench dynamics of the 2d XY model. J. Stat. Mech. 2011, P02032 (2011).

    Article  Google Scholar 

  36. 36.

    Zwierlein, M. W., Schirotzek, A., Schunck, C. H. & Ketterle, W. Vortices and superfluidity in a strongly interacting Fermi gas. Nature 435, 1047–1051 (2005).

    Article  ADS  Google Scholar 

Download references


We thank A. del Campo for discussions. This work was supported by the Institute for Basic Science in Korea (grant no. IBS-R009-D1) and the National Research Foundation of Korea (grant no. NRF-2018R1A2B3003373). J.W.P. acknowledges support from the POSCO Science Fellowship of the POSCO TJ Park Foundation.

Author information




J.W.P. and Y.S. conceived the idea. B.K. and J.W.P. performed the experiment and data analysis. J.W.P. and B.K. wrote the manuscript, and all authors discussed the results and commented on the manuscript. J.W.P. and Y.S. supervised the project.

Corresponding authors

Correspondence to Jee Woo Park or Y. Shin.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information: Nature Physics thanks Nikolaos Proukakis and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Materials

Supplementary Figs. 1–5, refs. 1–5 and text.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ko, B., Park, J.W. & Shin, Y. Kibble–Zurek universality in a strongly interacting Fermi superfluid. Nat. Phys. 15, 1227–1231 (2019).

Download citation

Further reading


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