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  • Featured in Physics
  • Open Access

Temperature Dependence of p-Wave Contacts in a Harmonically Trapped Fermi Gas

Kenta Nagase, Hikaru Takahashi, Soki Oshima, and Takashi Mukaiyama*

  • *Contact author: mukaiyama@phys.sci.isct.ac.jp

Phys. Rev. Lett. 136, 013402 – Published 8 January, 2026

DOI: https://doi.org/10.1103/3mxj-ym4b

Abstract

We study the dependence of the p-wave contact on the Fermi temperature TF and reduced temperature T/TF based on the number of closed-channel molecules. From the anisotropic pattern of dissociated molecules, we resolve the narrow m=0 and m=±1 dipolar splitting of the p-wave Feshbach resonance in Li6, enabling the independent determination of the contact for all three m components. For each component, we identify a near-resonant scaling with TF, indicating the contribution of the normalized effective range kFRe. In addition, we show that the peak contacts observed near resonance increase as T/TF is lowered, a trend that is accurately captured by estimates based on the second-order virial expansion. Our results, together with estimates from the p-wave virial expansion, provide a route toward a complete understanding of the thermodynamics of resonantly enhanced p-wave Fermi gases.

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synopsis

Elusive Quantum Interactions Tracked During Cooling

Published 8 January, 2026

The temperature dependence of so-called p-wave interactions in an ultracold atomic gas has been measured for the first time.

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References (59)

  1. S. Tan, Ann. Phys. (Amsterdam) 323, 2952 (2008).
  2. S. Tan, Ann. Phys. (Amsterdam) 323, 2971 (2008).
  3. S. Tan, Ann. Phys. (Amsterdam) 323, 2987 (2008).
  4. J. T. Stewart, J. P. Gaebler, T. E. Drake, and D. S. Jin, Phys. Rev. Lett. 104, 235301 (2010).
  5. G. B. Partridge, K. E. Strecker, R. I. Kamar, M. W. Jack, and R. G. Hulet, Phys. Rev. Lett. 95, 020404 (2005).
  6. E. D. Kuhnle, H. Hu, X.-J. Liu, P. Dyke, M. Mark, P. D. Drummond, P. Hannaford, and C. J. Vale, Phys. Rev. Lett. 105, 070402 (2010).
  7. S. Laurent, M. Pierce, M. Delehaye, T. Yefsah, F. Chevy, and C. Salomon, Phys. Rev. Lett. 118, 103403 (2017).
  8. Y. Sagi, T. E. Drake, R. Paudel, R. Chapurin, and D. S. Jin, Phys. Rev. Lett. 114, 075301 (2015).
  9. C. Shkedrov, Y. Florshaim, G. Ness, A. Gandman, and Y. Sagi, Phys. Rev. Lett. 121, 093402 (2018).
  10. Y. Sagi, T. E. Drake, R. Paudel, and D. S. Jin, Phys. Rev. Lett. 109, 220402 (2012).
  11. S. Hoinka, M. Lingham, K. Fenech, H. Hu, C. J. Vale, J. E. Drut, and S. Gandolfi, Phys. Rev. Lett. 110, 055305 (2013).
  12. E. D. Kuhnle, S. Hoinka, P. Dyke, H. Hu, P. Hannaford, and C. J. Vale, Phys. Rev. Lett. 106, 170402 (2011).
  13. B. Mukherjee, P. B. Patel, Z. Yan, R. J. Fletcher, J. Struck, and M. W. Zwierlein, Phys. Rev. Lett. 122, 203402 (2019).
  14. K. G. S. Xie, C. J. Dale, K. P. Grehan, M. F. Wang, T. Enss, P. S. Julienne, Z. Yu, and J. H. Thywissen, arXiv:2506.13707.
  15. S. Nascimbène, N. Navon, K. J. Jiang, F. Chevy, and C. Salomon, Nature (London) 463, 1057 (2010).
  16. N. Navon, S. Nascimbène, F. Chevy, and C. Salomon, Science 328, 729 (2010).
  17. M. Horikoshi, S. Nakajima, M. Ueda, and T. Mukaiyama, Science 327, 442 (2010).
  18. M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, Science 335, 563 (2012).
  19. M. He, S. Zhang, H. M. Chan, and Q. Zhou, Phys. Rev. Lett. 116, 045301 (2016).
  20. Z. Yu, J. H. Thywissen, and S. Zhang, Phys. Rev. Lett. 115, 135304 (2015).
  21. Z. Yu, J. H. Thywissen, and S. Zhang, Phys. Rev. Lett. 117, 019901(E) (2016).
  22. S. M. Yoshida and M. Ueda, Phys. Rev. Lett. 115, 135303 (2015).
  23. S.-G. Peng, X.-J. Liu, and H. Hu, Phys. Rev. A 94, 063651 (2016).
  24. D. Inotani and Y. Ohashi, Phys. Rev. A 98, 023603 (2018).
  25. F. Qin, X. Cui, and W. Yi, Phys. Rev. A 94, 063616 (2016).
  26. Y.-C. Zhang and S. Zhang, Phys. Rev. A 95, 023603 (2017).
  27. X. Yin, X.-W. Guan, Y. Zhang, H. Su, and S. Zhang, Phys. Rev. A 98, 023605 (2018).
  28. J. Maki, C. J. Dale, J. H. Thywissen, and S. Zhang, Phys. Rev. A 110, 053314 (2024).
  29. J. Yao and S. Zhang, Phys. Rev. A 97, 043612 (2018).
  30. C. Luciuk, S. Trotzky, S. Smale, Z. Yu, S. Zhang, and J. H. Thywissen, Nat. Phys. 12, 599 (2016).
  31. K. G. Jackson, C. J. Dale, J. Maki, K. G. S. Xie, B. A. Olsen, D. J. M. Ahmed-Braun, S. Zhang, and J. H. Thywissen, Phys. Rev. X 13, 021013 (2023).
  32. C. J. Dale, K. G. S. Xie, K. Pond Grehan, S. Zhang, J. Maki, and J. H. Thywissen, Phys. Rev. A 110, L051302 (2024).
  33. K. Nagase, S. Oshima, H. Takahashi, and T. Mukaiyama, Phys. Rev. A 111, 013314 (2025).
  34. J. R. Taylor, Scattering Theory: The Quantum Theory of Nonrelativistic Collisions (Wiley, New York, 1972).
  35. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Course of Theoretical Physics Vol. 3 (Butterworth-Heinemann, London, 1999).
  36. C. Ticknor, C. A. Regal, D. S. Jin, and J. L. Bohn, Phys. Rev. A 69, 042712 (2004).
  37. J. P. Gaebler, J. T. Stewart, J. L. Bohn, and D. S. Jin, Phys. Rev. Lett. 98, 200403 (2007).
  38. M. Iskin and C. A. R. Sá de Melo, Phys. Rev. Lett. 96, 040402 (2006).
  39. C.-H. Cheng and S.-K. Yip, Phys. Rev. Lett. 95, 070404 (2005).
  40. V. Gurarie and L. Radzihovsky, Ann. Phys. (Amsterdam) 322, 2 (2007).
  41. M. Y. Kagan and D. V. Efremov, J. Exp. Theor. Phys. 110, 426 (2010).
  42. J. Levinsen, P. Massignan, F. Chevy, and C. Lobo, Phys. Rev. Lett. 109, 075302 (2012).
  43. S. Peng, S. Peng, L. Ren, S. Liu, B. Liu, J. Li, and L. Luo, arXiv:2505.22409.
  44. M. Waseem, Z. Zhang, J. Yoshida, K. Hattori, T. Saito, and T. Mukaiyama, J. Phys. B 49, 204001 (2016).
  45. T. Volz, S. Dürr, N. Syassen, G. Rempe, E. van Kempen, and S. Kokkelmans, Phys. Rev. A 72, 010704(R) (2005).
  46. N. R. Thomas, N. Kjærgaard, P. S. Julienne, and A. C. Wilson, Phys. Rev. Lett. 93, 173201 (2004).
  47. See Supplemental Material at http://link.aps.org/supplemental/10.1103/3mxj-ym4b for more details.
  48. M. Gerken, B. Tran, S. Häfner, E. Tiemann, B. Zhu, and M. Weidemüller, Phys. Rev. A 100, 050701(R) (2019).
  49. J. Fuchs, C. Ticknor, P. Dyke, G. Veeravalli, E. Kuhnle, W. Rowlands, P. Hannaford, and C. J. Vale, Phys. Rev. A 77, 053616 (2008).
  50. T. Nakasuji, J. Yoshida, and T. Mukaiyama, Phys. Rev. A 88, 012710 (2013).
  51. M. Waseem, T. Saito, J. Yoshida, and T. Mukaiyama, Phys. Rev. A 96, 062704 (2017).
  52. M. Waseem, J. Yoshida, T. Saito, and T. Mukaiyama, Phys. Rev. A 98, 020702(R) (2018).
  53. X.-J. Liu, H. Hu, and P. D. Drummond, Phys. Rev. Lett. 102, 160401 (2009).
  54. H. Hu, X.-J. Liu, and P. D. Drummond, New J. Phys. 13, 035007 (2011).
  55. X.-J. Liu, Phys. Rep. 524, 37 (2013).
  56. S.-G. Peng, S.-Q. Li, P. D. Drummond, and X.-J. Liu, Phys. Rev. A 83, 063618 (2011).
  57. C.-X. Zhang, S.-G. Peng, and K. Jiang, Phys. Rev. A 98, 043619 (2018).
  58. K. Kanjilal and D. Blume, Phys. Rev. A 70, 042709 (2004).
  59. Kenta Nagase, Dataset for “Temperature dependence of p-wave contacts in a harmonically trapped Fermi gas”, Zenodo, v1, 10.5281/zenodo.17901716 (2025).

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