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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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Fig. 1: Inelastic loss spectroscopy of 41K atoms in the vicinity of the d-wave shape resonance.
Fig. 2: Binding energy measurement of d-wave molecules.
Fig. 3: Lifetime of 41K atoms in the vicinity of the shape resonance.
Fig. 4: Collective oscillations of the radial radius of the BEC after magnetic field ramping across the shape resonance.
Fig. 5: Normalized remaining final number Nf and relative oscillation amplitude δexp as a function of ramp speed v.

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

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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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).

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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.

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

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

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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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