Letter | Published:

# Universal prethermal dynamics of Bose gases quenched to unitarity

## Abstract

Understanding strongly correlated phases of matter, such as the quark–gluon plasma and neutron stars, and in particular the dynamics of such systems, for example, following a Hamiltonian quench (a sudden change in some Hamiltonian parameter, such as the strength of interparticle interactions) is a fundamental challenge in modern physics. Ultracold atomic gases are excellent quantum simulators for these problems, owing to their tunable interparticle interactions and experimentally resolvable intrinsic timescales. In particular, they provide access to the unitary regime, in which the interactions are as strong as allowed by quantum mechanics. This regime has been extensively studied in Fermi gases1,2. The less-explored unitary Bose gases3,4,5,6,7,8,9,10,11 offer possibilities12 such as universal physics controlled solely by the gas density13,14 and new forms of superfluidity15,16,17. Here, through momentum- and time-resolved studies, we explore degenerate and thermal homogeneous Bose gases quenched to unitarity. In degenerate samples, we observe universal post-quench dynamics in agreement with the emergence of a prethermal state18,19,20,21,22,23,24 with a universal non-zero condensed fraction22,24. In thermal gases, the dynamic and thermodynamic properties generally depend on the gas density and the temperature, but we find that they can still be expressed in terms of universal dimensionless functions. Surprisingly, we find that the total quench-induced correlation energy is independent of the gas temperature. These measurements provide quantitative benchmarks and challenges for the theory of unitary Bose gases.

## Access optionsAccess options

from\$8.99

All prices are NET prices.

## Data availability

The data that support the findings of this study are available in the Apollo repository (https://doi.org/10.17863/CAM.30242). Any additional information is available from the corresponding authors on reasonable request.

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

## References

1. 1.

Zwerger, W. (ed.) The BCS-BEC Crossover and the Unitary Fermi Gas (Springer, Berlin, 2011).

2. 2.

Zwierlein, M. W. in Novel Superfluids Vol. 2 (eds Bennemann, K.-H. & Ketterson, J. B.) Ch. 18 (Oxford Univ. Press, Oxford, 2014).

3. 3.

Navon, N. et al. Dynamics and thermodynamics of the low-temperature strongly interacting Bose gas. Phys. Rev. Lett. 107, 135301 (2011).

4. 4.

Rem, B. S. et al. Lifetime of the Bose gas with resonant interactions. Phys. Rev. Lett. 110, 163202 (2013).

5. 5.

Fletcher, R. J., Gaunt, A. L., Navon, N., Smith, R. P. & Hadzibabic, Z. Stability of a Unitary Bose Gas. Phys. Rev. Lett. 111, 125303 (2013).

6. 6.

Makotyn, P., Klauss, C. E., Goldberger, D. L., Cornell, E. A. & Jin, D. S. Universal dynamics of a degenerate unitary Bose gas. Nat. Phys. 10, 116–119 (2014).

7. 7.

Eismann, U. et al. Universal loss dynamics in a unitary Bose gas. Phys. Rev. X 6, 021025 (2016).

8. 8.

Fletcher, R. J. et al. Two- and three-body contacts in the unitary Bose gas. Science 355, 377–380 (2017).

9. 9.

Klauss, C. E. et al. Observation of Efimov molecules created from a resonantly interacting Bose gas. Phys. Rev. Lett. 119, 143401 (2017).

10. 10.

Eigen, C. et al. Universal scaling laws in the dynamics of a homogeneous unitary Bose gas. Phys. Rev. Lett. 119, 250404 (2017).

11. 11.

Fletcher, R. J. et al. Elliptic flow in a strongly interacting normal Bose gas. Phys. Rev. A 98, 011601 (2018).

12. 12.

Chevy, F. & Salomon, C. Strongly correlated Bose gases. J. Phys. B 49, 192001 (2016).

13. 13.

Cowell, S. et al. Cold Bose gases with large scattering lengths. Phys. Rev. Lett. 88, 210403 (2002).

14. 14.

Ho, T.-L. Universal thermodynamics of degenerate quantum gases in the unitarity limit. Phys. Rev. Lett. 92, 090402 (2004).

15. 15.

Radzihovsky, L., Park, J. & Weichman, P. B. Superfluid transitions in bosonic atom-molecule mixtures near a Feshbach resonance. Phys. Rev. Lett. 92, 160402 (2004).

16. 16.

Romans, M. W. J., Duine, R. A., Sachdev, S. & Stoof, H. T. C. Quantum phase transition in an atomic Bose gas with a Feshbach resonance. Phys. Rev. Lett. 93, 020405 (2004).

17. 17.

Piatecki, S. & Krauth, W. Efimov-driven phase transitions of the unitary Bose gas. Nat. Commun. 5, 3503 (2014).

18. 18.

Berges, J., Borsányi, Sz. & Wetterich, C. Prethermalization. Phys. Rev. Lett. 93, 142002 (2004).

19. 19.

Gring, M. et al. Relaxation and prethermalization in an isolated quantum system. Science 337, 1318–1322 (2012).

20. 20.

Yin, X. & Radzihovsky, L. Quench dynamics of a strongly interacting resonant Bose gas. Phys. Rev. A 88, 063611 (2013).

21. 21.

Sykes, A. G. et al. Quenching to unitarity: quantum dynamics in a three-dimensional Bose gas. Phys. Rev. A 89, 021601 (2014).

22. 22.

Kain, B. & Ling, H. Y. Nonequilibrium states of a quenched Bose gas. Phys. Rev. A 90, 063626 (2014).

23. 23.

Rançon, A. & Levin, K. Equilibrating dynamics in quenched Bose gases: characterizing multiple time regimes. Phys. Rev. A 90, 021602 (2014).

24. 24.

Yin, X. & Radzihovsky, L. Postquench dynamics and prethermalization in a resonant Bose gas. Phys. Rev. A 93, 033653 (2016).

25. 25.

Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225–1286 (2010).

26. 26.

Efimov, V. Energy levels arising from resonant two-body forces in a three-body system. Phys. Lett. B 33, 563–564 (1970).

27. 27.

Kraemer, T. et al. Evidence for Efimov quantum states in an ultracold gas of caesium atoms. Nature 440, 315–318 (2006).

28. 28.

Smith, D. H., Braaten, E., Kang, D. & Platter, L. Two-body and three-body contacts for identical bosons near unitarity. Phys. Rev. Lett. 112, 110402 (2014).

29. 29.

Comparin, T. & Krauth, W. Momentum distribution in the unitary Bose gas from first principles. Phys. Rev. Lett. 117, 225301 (2016).

30. 30.

Colussi, V. E., Corson, J. P. & D’Incao, J. P. Dynamics of three-body correlations in quenched unitary Bose gases. Phys. Rev. Lett. 120, 100401 (2018).

31. 31.

D’Incao, J. P., Wang, J. & Colussi, V. E. Efimov physics in quenched unitary Bose gases. Phys. Rev. Lett. 121, 023401 (2018).

32. 32.

Tan, S. Energetics of a strongly correlated Fermi gas. Ann. Phys. 323, 2952–2970 (2008).

33. 33.

Li, W. & Ho, T.-L. Bose gases near unitarity. Phys. Rev. Lett. 108, 195301 (2012).

34. 34.

Prüfer, M. et al. Observation of universal dynamics in a spinor Bose gas far from equilibrium. Nature https://doi.org/10.1038/s41586-018-0659-0 (2018).

35. 35.

Erne, S., Bücker, R., Gasenzer, T., Berges, J. & Schmiedmayer, J. Universal dynamics in an isolated one-dimensional Bose gas far from equilibrium. Nature https://doi.org/10.1038/s41586-018-0667-0 (2018).

36. 36.

Gaunt, A. L., Schmidutz, T. F., Gotlibovych, I., Smith, R. P. & Hadzibabic, Z. Bose–Einstein condensation of atoms in a uniform potential. Phys. Rev. Lett. 110, 200406 (2013).

37. 37.

Eigen, C. et al. Observation of weak collapse in a Bose–Einstein condensate. Phys. Rev. X 6, 041058 (2016).

## Acknowledgements

We thank R. Fletcher, N. Navon and T. Hilker for discussions and comments on the manuscript. This work was supported by the Royal Society, EPSRC (grant numbers EP/N011759/1 and EP/P009565/1), ERC (QBox), AFOSR and ARO. R.L. acknowledges support from the EU Marie Curie programme (grant number MSCA-IF-2015 704832) and Churchill College, Cambridge. E.A.C. acknowledges hospitality and support from Trinity College, Cambridge.

### Reviewer information

Nature thanks M. Kolodrubetz and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

### Author notes

• Raphael Lopes

Present address: Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, UPMC-Sorbonne Université, Paris, France

### Affiliations

1. #### Cavendish Laboratory, University of Cambridge, Cambridge, UK

• Christoph Eigen
• , Jake A. P. Glidden
• , Raphael Lopes
• , Robert P. Smith
2. #### JILA, National Institute of Standards and Technology, University of Colorado, Boulder, CO, USA

• Eric A. Cornell
3. #### Department of Physics, University of Colorado, Boulder, CO, USA

• Eric A. Cornell
4. #### Clarendon Laboratory, University of Oxford, Oxford, UK

• Robert P. Smith

### Contributions

C.E., J.A.P.G. and R.L. collected the data. C.E. analysed the data and produced the figures. C.E., E.A.C., R.P.S. and Z.H. interpreted the data and wrote the manuscript.

### Competing interests

The authors declare no competing interests.

### Corresponding authors

Correspondence to Christoph Eigen or Zoran Hadzibabic.

## Extended data figures and tables

1. ### Extended Data Fig. 1 Extrapolation of $${\bar{{\boldsymbol{n}}}}_{{\boldsymbol{k}}}{{\boldsymbol{k}}}_{{\boldsymbol{n}}}^{{\bf{3}}}$$ in a degenerate gas to lower k/kn.

Solid symbols show directly measured values (also shown in Fig. 2b), here combining the data for all three BEC densities. Open symbols show experimentally extrapolated values, for all three densities, as described in Methods. The solid line is the same as in Fig. 2b.