# Degenerate Bose gases near a d-wave shape resonance

## Abstract

Understanding quantum many-body systems with strong interactions and unconventional phases therein is one of the most challenging tasks in physics. In cold atom physics, this has been a focused research topic for nearly two decades, where strong interactions are naturally created and well manipulated by bringing the system close to a scattering resonance. However, most of the studies thus far have been limited to the s-wave resonance. Here, we report the experimental observation of a tunable and broad d-wave shape resonance in a quantum degenerate 41K gas, hallmarked by the fact that the molecular binding energies are split into three branches. The measured lifetime in the resonance regime is found to be much longer than the characteristic timescale for many-body relaxations. The analysis of the breathing mode, excited by ramping through the resonance, suggests that a low-temperature atom–molecule mixture is produced. Our system offers great promise for studying a d-wave molecular superfluid.

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## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

## References

1. 1.

Landau, L. D. & Lifshitz, E. M. Course of Theoretical Physics, Vol. 9., Statistical Physics, Part 2 (Pergamon Press, Oxford, 1980).

2. 2.

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

3. 3.

Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).

4. 4.

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

5. 5.

Lahaye, T., Menotti, C., Santos, L., Lewenstein, M. & Pfau, T. The physics of dipolar bosonic quantum gases. Rep. Prog. Phys. 72, 126401 (2009).

6. 6.

Navon, N., Nascimbène, S., Chevy, F. & Salomon, C. The equation of state of a low-temperature Fermi gas with tunable interactions. Science 328, 729–732 (2010).

7. 7.

Cao, C. et al. Universal quantum viscosity in a unitary Fermi gas. Science 331, 58–61 (2010).

8. 8.

Horikoshi, M., Nakajima, S., Ueda, M. & Mukaiyama, T. Measurement of universal thermodynamic functions for a unitary Fermi gas. Science 327, 442–445 (2010).

9. 9.

Ku, M. J. H., Sommer, A. T., Cheuk, L. W. & Zwierlein, M. W. Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas. Science 335, 563–567 (2012).

10. 10.

Stadler, D., Krinner, S., Meineke, J., Brantut, J.-P. & Esslinger, T. Observing the drop of resistance in the flow of a superfluid Fermi gas. Nature 491, 736–739 (2012).

11. 11.

Sidorenkov, L. A. et al. Second sound and the superfluid fraction in a Fermi gas with resonant interactions. Nature 498, 78–81 (2013).

12. 12.

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).

13. 13.

Bardon, A. B. et al. Transverse demagnetization dynamics of a unitary Fermi gas. Science 344, 722–724 (2014).

14. 14.

Deng, S. et al. Observation of the Efimovian expansion in scale-invariant Fermi gases. Science 353, 371–374 (2016).

15. 15.

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

16. 16.

Zhang, J. et al. P-wave Feshbach resonances of ultracold 6Li. Phys. Rev. A 70, 030702 (2004).

17. 17.

Gaebler, J. P., Stewart, J. T., Bohn, J. L. & Jin, D. S. p-Wave Feshbach molecules. Phys. Rev. Lett. 98, 200403 (2007).

18. 18.

Luciuk, C. et al. Evidence for universal relations describing a gas with p-wave interactions. Nat. Phys. 12, 599–605 (2016).

19. 19.

Volz, T. et al. Feshbach spectroscopy of a shape resonance. Phys. Rev. A 72, 010704 (2005).

20. 20.

Covey, J. P. et al. Doublon dynamics and polar molecule production in an optical lattice. Nat. Commun. 7, 11279 (2016).

21. 21.

Cui, Y. et al. Observation of broad d-wave Feshbach resonances with a triplet structure. Phys. Rev. Lett. 119, 203402 (2017).

22. 22.

Gao, B., Tiesinga, E., Williams, C. J. & Julienne, P. S. Multichannel quantum-defect theory for slow atomic collisions. Phys. Rev. A 72, 042719 (2005).

23. 23.

Gao, B. Analytic description of atomic interaction at ultracold temperatures: the case of a single channel. Phys. Rev. A 80, 012702 (2009).

24. 24.

Gao, B. Analytic description of atomic interaction at ultracold temperatures. II. Scattering around a magnetic Feshbach resonance. Phys. Rev. A 84, 022706 (2011).

25. 25.

Yao, X.-C. et al. Observation of coupled vortex lattices in a mass-imbalance Bose and Fermi superfluid mixture. Phys. Rev. Lett. 117, 145301 (2016).

26. 26.

Chen, H.-Z. et al. Production of large 41K Bose–Einstein condensates using D1 gray molasses. Phys. Rev. A 94, 033408 (2016).

27. 27.

Wu, Y.-P. et al. A quantum degenerate Bose–Fermi mixture of 41K and 6Li. J. Phys. B 50, 094001 (2017).

28. 28.

Wang, J., D’Incao, J. P., Wang, Y. & Greene, C. H. Universal three-body recombination via resonant d-wave interactions. Phys. Rev. A 86, 062511 (2012).

29. 29.

Reinaudi, G., Lahaye, T., Wang, Z. & Guéry-Odelin, D. Strong saturation absorption imaging of dense clouds of ultracold atoms. Opt. Lett. 32, 3143 (2007).

30. 30.

Regal, C. A., Ticknor, C., Bohn, J. L. & Jin, D. S. Tuning p-wave interactions in an ultracold Fermi gas of atoms. Phys. Rev. Lett. 90, 053201 (2003).

31. 31.

Thompson, S. T., Hodby, E. & Wieman, C. E. Ultracold molecule production via a resonant oscillating magnetic field. Phys. Rev. Lett. 95, 190404 (2005).

32. 32.

Falke, S. et al. Potassium ground-state scattering parameters and Born–Oppenheimer potentials from molecular spectroscopy. Phys. Rev. A 78, 012503 (2008).

33. 33.

Zaccanti, M. et al. Observation of an Efimov spectrum in an atomic system. Nat. Phys. 5, 586–591 (2009).

34. 34.

Herbig, J. et al. Preparation of a pure molecular quantum gas. Science 301, 1510–1513 (2003).

35. 35.

Regal, C. A., Ticknor, C., Bohn, J. L. & Jin, D. S. Creation of ultracold molecules from a Fermi gas of atoms. Nature 424, 47–50 (2003).

36. 36.

Pérez-Garca, V. M., Michinel, H., Cirac, J. I., Lewenstein, M. & Zoller, P. Low energy excitations of a Bose–Einstein condensate: a time-dependent variational analysis. Phys. Rev. Lett. 77, 5320–5323 (1996).

37. 37.

Stringari, S. Collective excitations of a trapped Bose-condensed gas. Phys. Rev. Lett. 77, 2360–2363 (1996).

38. 38.

Yao, J., Zhang, P., Qi, R. & Zhai, H. Three-body problem of bosons near a d-wave resonance. Phys. Rev. A 99, 012701 (2019).

39. 39.

Zhang, P., Zhang, S. & Yu, Z. Effective theory and universal relations for Fermi gases near a d-wave interaction resonance. Phys. Rev. A 95, 043609 (2017).

## Acknowledgements

We thank C. Chin, B. Gao and Y. Deng for discussions. This work has been supported by the National Key R&D Program of China (grants nos. 2018YFA0306501, 2018YFA0306502 and 2016YFA0301600), NSFC of China (grants nos. 11874340, 11774426, 11434011, 11674393, 11734010 and 11425417), the CAS, the Anhui Initiative in Quantum Information Technologies, the Fundamental Research Funds for the Central Universities (grant no. WK2340000081) and the Research Funds of Renmin University of China (grants nos. 16XNLQ03 and 17XNH054).

## Author information

Authors

### Contributions

X.-C.Y., Y.-A.C. and J.-W.P. conceived the research. X.-C.Y., X.-P.L., X.-Q.W.,Y.-X.W., Y.-P.W. and H.-Z.C. performed the experiment. R.Q., P.Z. and H.Z. contributed the theory part of this work. All authors discussed the results and wrote the manuscript.

### Corresponding authors

Correspondence to Hui Zhai or Yu-Ao Chen or Jian-Wei Pan.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary Text, Supplementary Figures 1–2 and Supplementary References.

## Rights and permissions

Reprints and Permissions

Yao, XC., Qi, R., Liu, XP. et al. Degenerate Bose gases near a d-wave shape resonance. Nat. Phys. 15, 570–576 (2019). https://doi.org/10.1038/s41567-019-0455-2

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