Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Long-range states in collisions of ultracold molecules

James F. E. Croft1, Brian K. Kendrick2, and Jeremy M. Hutson1,*

  • 1Joint Quantum Centre (JQC) Durham-Newcastle, Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
  • 2Theoretical Division (T-1, MS B221), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

  • *Contact author: j.m.hutson@durham.ac.uk

Phys. Rev. Research 8, 043087 – Published 23 October, 2026

DOI: https://doi.org/10.1103/fvjz-ymg4

Abstract

We use coupled-channel calculations to explore the nature of near-threshold bound states in a simplified model of Rb+KRb. This is a prototype for systems with very strong coupling at short range and chaotic behavior for the short-range states. We find that there are states with strong long-range character that exist close to threshold and probably persist to depths at least 100 GHz below each threshold. These states are only weakly coupled to the short-range states and do not form part of the chaotic manifold. Since they spend little time at short range, they are relatively insensitive to destruction by laser light. They can thus have long lifetimes that are unrelated to the density of states and can cause narrow Feshbach resonances when the states are shifted across thresholds by external fields.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (75)

  1. S. Ospelkaus, K.-K. Ni, D. Wang, M. H. G. de Miranda, B. Neyenhuis, G. Quéméner, P. S. Julienne, J. L. Bohn, D. S. Jin, and J. Ye, Quantum-state controlled chemical reactions of ultracold KRb molecules, Science 327, 853 (2010).
  2. T. Takekoshi, L. Reichsöllner, A. Schindewolf, J. M. Hutson, C. R. Le Sueur, O. Dulieu, F. Ferlaino, R. Grimm, and H.-C. Nägerl, Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state, Phys. Rev. Lett. 113, 205301 (2014).
  3. J. W. Park, S. A. Will, and M. W. Zwierlein, Ultracold dipolar gas of fermionic Na23K40 molecules in their absolute ground state, Phys. Rev. Lett. 114, 205302 (2015).
  4. M. Guo, X. Ye, J. He, G. Quéméner, and D. Wang, High-resolution internal state control of ultracold Na23Rb87 molecules, Phys. Rev. A 97, 020501(R) (2018).
  5. Y. Liu and K.-K. Ni, Bimolecular chemistry in the ultracold regime, Annu. Rev. Phys. Chem. 73, 73 (2022).
  6. B. Zhao and J.-W. Pan, Quantum control of reactions and collisions at ultralow temperatures, Chem. Soc. Rev. 51, 1685 (2022).
  7. K.-K. Ni, S. Ospelkaus, M. H. G. de Miranda, A. Pe’er, B. Neyenhuis, J. J. Zirbel, S. Kotochigova, P. S. Julienne, D. S. Jin, and J. Ye, A high phase-space-density gas of polar molecules in the rovibrational ground state, Science 322, 231 (2008).
  8. J. G. Danzl, M. J. Mark, E. Haller, M. Gustavsson, R. Hart, J. Aldegunde, J. M. Hutson, and H.-C. Nägerl, An ultracold, high-density sample of rovibronic ground-state molecules in an optical lattice, Nat. Phys. 6, 265 (2010).
  9. T. Langen, G. Valtolina, D. Wang, and J. Ye, Quantum state manipulation and cooling of ultracold molecules, Nat. Phys. 20, 702 (2024).
  10. S. Ospelkaus, K.-K. Ni, G. Quéméner, B. Neyenhuis, D. Wang, M. H. G. de Miranda, J. L. Bohn, J. Ye, and D. S. Jin, Controlling the hyperfine state of rovibronic ground-state polar molecules, Phys. Rev. Lett. 104, 030402 (2010).
  11. P. D. Gregory, J. Aldegunde, J. M. Hutson, and S. L. Cornish, Controlling the rotational and hyperfine state of ultracold Rb87Cs133 molecules, Phys. Rev. A 94, 041403(R) (2016).
  12. S. L. Cornish, M. R. Tarbutt, and K. R. A. Hazzard, Quantum computation and quantum simulation with ultracold molecules, Nat. Phys. 20, 730 (2024).
  13. M. Mayle, B. P. Ruzic, and J. L. Bohn, Statistical aspects of ultracold resonant scattering, Phys. Rev. A 85, 062712 (2012).
  14. M. Mayle, G. Quéméner, B. P. Ruzic, and J. L. Bohn, Scattering of ultracold molecules in the highly resonant regime, Phys. Rev. A 87, 012709 (2013).
  15. X. Ye, M. Guo, M. L. González-Martínez, G. Quéméner, and D. Wang, Collisions of ultracold Na23Rb87 molecules with controlled chemical reactivities, Sci. Adv. 4, eaaq0083 (2018).
  16. P. D. Gregory, M. D. Frye, J. A. Blackmore, E. M. Bridge, R. Sawant, J. M. Hutson, and S. L. Cornish, Sticky collisions of ultracold RbCs molecules, Nat. Commun. 10, 3104 (2019).
  17. R. Bause, A. Christianen, A. Schindewolf, I. Bloch, and X.-Y. Luo, Ultracold sticky collisions: Theoretical and experimental status, J. Phys. Chem. A 127, 729 (2023).
  18. M.-G. Hu, Y. Liu, D. D. Grimes, Y.-W. Lin, A. H. Gheorghe, R. Vexiau, N. Bouloufa-Maafa, O. Dulieu, T. Rosenband, and K.-K. Ni, Direct observation of bimolecular reactions of ultracold KRb molecules, Science 366, 1111 (2019).
  19. A. Christianen, M. W. Zwierlein, G. C. Groenenboom, and T. Karman, Photoinduced two-body loss of ultracold molecules, Phys. Rev. Lett. 123, 123402 (2019).
  20. Y. Liu, M.-G. Hu, M. A. Nichols, D. D. Grimes, T. Karman, H. Guo, and K.-K. Ni, Photo-excitation of long-lived transient intermediates in ultracold reactions, Nat. Phys. 16, 1132 (2020).
  21. J. F. E. Croft, N. Balakrishnan, and B. K. Kendrick, Long-lived complexes and signatures of chaos in ultracold K2+Rb collisions, Phys. Rev. A 96, 062707 (2017).
  22. A. Christianen, T. Karman, and G. C. Groenenboom, A quasiclassical method for calculating the density of states of ultracold collision complexes, Phys. Rev. A 100, 032708 (2019).
  23. M. D. Frye and J. M. Hutson, Complexes formed in collisions between ultracold alkali-metal diatomic molecules and atoms, New J. Phys. 23, 125008 (2021).
  24. J. F. E. Croft, J. L. Bohn, and G. Quéméner, Anomalous lifetimes of ultracold complexes decaying into a single channel, Phys. Rev. A 107, 023304 (2023).
  25. K. Jachymski, M. Gronowski, and M. Tomza, Collisional losses of ultracold molecules due to intermediate complex formation, Phys. Rev. A. 106, L041301 (2022).
  26. M. P. Man, G. C. Groenenboom, and T. Karman, Symmetry breaking in sticky collisions between ultracold molecules, Phys. Rev. Lett. 129, 243401 (2022).
  27. P. D. Gregory, J. A. Blackmore, S. L. Bromley, and S. L. Cornish, Loss of ultracold Rb87Cs133 molecules via optical excitation of long-lived two-body collision complexes, Phys. Rev. Lett. 124, 163402 (2020).
  28. R. Bause, A. Schindewolf, R. Tao, M. Duda, X.-Y. Chen, G. Quéméner, T. Karman, A. Christianen, I. Bloch, and X.-Y. Luo, Collisions of ultracold molecules in bright and dark optical dipole traps, Phys. Rev. Res. 3, 033013 (2021).
  29. P. Gersema, K. K. Voges, M. Meyer zum Alten Borgloh, L. Koch, T. Hartmann, A. Zenesini, S. Ospelkaus, J. Lin, J. He, and D. Wang, Probing photoinduced two-body loss of ultracold nonreactive bosonic Na23Rb87 and Na23K39 molecules, Phys. Rev. Lett. 127, 163401 (2021).
  30. M. Guo, X. Ye, J. He, M. L. González-Martínez, R. Vexiau, G. Quéméner, and D. Wang, Dipolar collisions of ultracold ground-state bosonic molecules, Phys. Rev. X 8, 041044 (2018).
  31. Z. Idziaszek and P. S. Julienne, Universal rate constants for reactive collisions of ultracold molecules, Phys. Rev. Lett. 104, 113202 (2010).
  32. Z. Idziaszek, G. Quéméner, J. L. Bohn, and P. S. Julienne, Simple quantum model of ultracold polar molecule collisions, Phys. Rev. A. 82, 020703(R) (2010).
  33. P. D. Gregory, J. A. Blackmore, F. Matthew D, L. M. Fernley, S. L. Bromley, J. M. Hutson, and S. L. Cornish, Molecule-molecule and atom-molecule collisions with ultracold RbCs molecules, New J. Phys. 23, 125004 (2021).
  34. K. K. Voges, P. Gersema, T. Hartmann, S. Ospelkaus, and A. Zenesini, Hyperfine dependent atom-molecule loss analyzed by the analytic solution of few-body loss equations, Phys. Rev. Res. 4, 023184 (2022).
  35. M. A. Nichols, Y.-X. Liu, L. Zhu, M.-G. Hu, Y. Liu, and K.-K. Ni, Detection of long-lived complexes in ultracold atom-molecule collisions, Phys. Rev. X 12, 011049 (2022).
  36. Y.-X. Liu, L. Zhu, J. Luke, M. C. Babin, M. Gronowski, H. Ladjimi, M. Tomza, J. L. Bohn, T. V. Tscherbul, and K.-K. Ni, Hyperfine-to-rotational energy transfer in ultracold atom–molecule collisions of Rb and KRb, Nat. Chem. 17, 688 (2025).
  37. H. Yang, D.-C. Zhang, L. Liu, Y.-X. Liu, J. Nan, B. Zhao, and J.-W. Pan, Observation of magnetically tunable Feshbach resonances in ultracold Na23K40+K40 collisions, Science 363, 261 (2019).
  38. X.-Y. Wang, M. D. Frye, Z. Su, J. Cao, L. Liu, D.-C. Zhang, H. Yang, J. M. Hutson, B. Zhao, C.-L. Bai, and J.-W. Pan, Magnetic Feshbach resonances in collisions of Na23K40 with K40, New J. Phys. 23, 115010 (2021).
  39. M. D. Frye, P. S. Julienne, and J. M. Hutson, Cold atomic and molecular collisions: Approaching the universal loss regime, New J. Phys. 17, 045019 (2015).
  40. M. D. Frye and J. M. Hutson, Long-range states and Feshbach resonances in collisions between ultracold alkali-metal diatomic molecules and atoms, Phys. Rev. Res. 5, 023001 (2023).
  41. Z. Su, H. Yang, J. Cao, X.-Y. Wang, J. Rui, B. Zhao, and J.-W. Pan, Resonant control of elastic collisions between Na23K40 molecules and K40 atoms, Phys. Rev. Lett. 129, 033401 (2022).
  42. H. Yang, J. Cao, Z. Su, J. Rui, B. Zhao, and J.-W. Pan, Creation of an ultracold gas of triatomic molecules from an atom–diatomic molecule mixture, Science 378, 1009 (2022).
  43. J. Cao, B.-Y. Wang, H. Yang, Z.-J. Fan, Z. Su, J. Rui, B. Zhao, and J.-W. Pan, Observation of photoassociation resonances in ultracold atom-molecule collisions, Phys. Rev. Lett. 132, 093403 (2024).
  44. M. M. zum Alten Borgloh, J. Heier, F. von Gierke, B. Shammout, E. Tiemann, L. Karpa, and S. Ospelkaus, Electric-field control of atom-molecule Feshbach resonances, arXiv:2602.23929.
  45. C. J. Ashton, M. S. Child, and J. M. Hutson, Rotational predissociation of the Ar-HCl van der Waals complex: Close-coupled scattering calculations, J. Chem. Phys. 78, 4025 (1983).
  46. J. F. E. Croft and J. L. Bohn, Long-lived complexes and chaos in ultracold molecular collisions, Phys. Rev. A. 89, 012714 (2014).
  47. J. Kłos, Q. Guan, H. Li, M. Li, E. Tiesinga, and S. Kotochigova, Roaming pathways and survival probability in real-time collisional dynamics of cold and controlled bialkali molecules, Sci. Rep. 11, 10598 (2021).
  48. J. F. E. Croft, C. Makrides, M. Li, A. Petrov, B. K. Kendrick, N. Balakrishnan, and S. Kotochigova, Universality and chaoticity in ultracold K + KRb chemical reactions, Nat. Commun. 8, 15897 (2017).
  49. R. J. LeRoy and R. B. Bernstein, Dissociation energy and long-range potential of diatomic molecules from vibrational spacings of higher levels, J. Chem. Phys. 52, 3869 (1970).
  50. B. Gao, Solutions of the Schrödinger equation for an attractive 1/r6 potential, Phys. Rev. A. 58, 1728 (1998).
  51. G. F. Gribakin and V. V. Flambaum, Calculation of the scattering length in atomic collisions using the semiclassical approximation, Phys. Rev. A. 48, 546 (1993).
  52. B. K. Kendrick, H. Li, J. Kłos, and S. Kotochigova, Non-adiabatic quantum interference and complex formation in ultracold collisions of Rb with KRb, Phys. Chem. Chem. Phys. 28, 9223 (2026).
  53. R. T Pack and G. A. Parker, Quantum reactive scattering in three dimensions using hypersperical (APH) coordinates. Theory, J. Chem. Phys. 87, 3888 (1987).
  54. B. K. Kendrick, R. T Pack, R. B. Walker, and E. F. Hayes, Hyperspherical surface functions for nonzero total angular momentum. I. Eckart singularities, J. Chem. Phys. 110, 6673 (1999).
  55. J. M. Hutson, BOUND computer program, version 1, Distributed by Collaborative Computational Project No. 6 of the UK Engineering and Physical Sciences Research Council, 1984.
  56. J. M. Hutson and C. R. Le Sueur, bound and field: Programs for calculating bound states of interacting pairs of atoms and molecules, Comput. Phys. Commun. 241, 1 (2019).
  57. J. M. Hutson and C. R. Le Sueur, molscat, bound and field, version 2023.0, GitHub, 2023, https://github.com/molscat/molscat.
  58. D. E. Manolopoulos, An improved log-derivative method for inelastic scattering, J. Chem. Phys. 85, 6425 (1986).
  59. M. H. Alexander and D. E. Manolopoulos, A stable linear reference potential algorithm for solution of the quantum close-coupled equations in molecular scattering theory, J. Chem. Phys. 86, 2044 (1987).
  60. A. E. Thornley and J. M. Hutson, Bound-state wavefunctions from coupled-channel calculations using log-derivative propagators: Application to spectroscopic intensities in Ar-HF, J. Chem. Phys. 101, 5578 (1994).
  61. B. Kendrick and R. T Pack, Geometric phase effects in the resonance spectrum, state-to-state transition probabilities and bound state spectrum of HO2, J. Chem. Phys. 106, 3519 (1997).
  62. B. R. Johnson, The renormalized Numerov method applied to calculating bound states of the coupled-channel Schrödinger equation, J. Chem. Phys. 69, 4678 (1978).
  63. J. M. Hutson, Coupled-channel methods for solving the bound-state Schrödinger equation, Comput. Phys. Commun. 84, 1 (1994).
  64. C. R. Le Sueur, J. F. E. Croft, and J. M. Hutson, Converging on bound states in coupled-channel calculations, J. Phys. Chem. A 130, 7602 (2026).
  65. E. P. Wigner, On the statistical distribution of the widths and spacings of nuclear resonance levels, Math. Proc. Cambridge Philos. Soc. 47, 790 (1951).
  66. F. J. Dyson, Statistical theory of the energy levels of complex systems. I, J. Math. Phys. 3, 140 (1962).
  67. M. V. Berry and M. Tabor, Level clustering in the regular spectrum, Proc. R. Soc. A 356, 375 (1977).
  68. T. Brody, A statistical measure for the repulsion of energy levels, Lett. Nuovo Cimento 7, 482 (1973).
  69. T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Wong, Random-matrix physics: Spectrum and strength fluctuations, Rev. Mod. Phys. 53, 385 (1981).
  70. M. V. Berry and M. Robnik, Semiclassical level spacings when regular and chaotic orbits coexist, J. Phys. A: Math. Gen. 17, 2413 (1984).
  71. T. Guhr, A. Müller–Groeling, and H. A. Weidenmüller, Random matrix theories in quantum physics: Common concepts, Phys. Rep. 299, 189 (1998).
  72. J. M. Hutson, Theory of cold atomic and molecular collisions, in Cold Molecules: Theory, Experiment, Applications, edited by R. V. Krems, W. C. Stwalley, and B. Friedrich (Taylor & Francis, London, 2009), pp. 3–37.
  73. B. Gao, Zero-energy bound or quasibound states and their implications for diatomic systems with an asymptotic van der Waals interaction, Phys. Rev. A. 62, 050702(R) (2000).
  74. D. A. Brue and J. M. Hutson, Prospects of forming molecules in 2Σ states by magnetoassociation of alkali-metal atoms with Yb, Phys. Rev. A. 87, 052709 (2013).
  75. J. M. Hutson, Long-range states in collisions of ultracold molecules [dataset], Durham University, 10.15128/r1m326m1814.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation