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Hyperfine-resolved optical spectroscopy of ultracold Rb87Cs133 molecules: The b3Π0 metastable state

Arpita Das*, Albert Li Tao, Luke M. Fernley†, Fritz von Gierke‡, Philip D. Gregory, and Simon L. Cornish§

Jeremy M. Hutson

Romain Vexiau and Olivier Dulieu

  • Department of Physics and Joint Quantum Centre (JQC) Durham-Newcastle, Durham University, Durham DH1 3LE, United Kingdom

  • Department of Chemistry and Joint Quantum Centre (JQC) Durham-Newcastle, Durham University, Durham DH1 3LE, United Kingdom

  • *Contact author: arpita.das@durham.ac.uk
  • †Present address: National Quantum Computing Centre, Didcot OX11 0QX, United Kingdom.
  • ‡Present address: Institut für Quantenoptik, Leibniz Universität Hannover, 30167 Hannover, Germany.
  • §Contact author: s.l.cornish@durham.ac.uk
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Phys. Rev. Research 8, 023005 – Published 1 April, 2026

DOI: https://doi.org/10.1103/yfs9-gghp

Abstract

Using an ultracold gas of Rb87Cs133 molecules, we perform hyperfine-resolved spectroscopy of transitions from the vibronic ground state to the lowest rovibrational states of the electronic state b3Π0 as a function of magnetic field. These transitions are spin forbidden, resulting in narrow linewidths, and feature near-diagonal Franck-Condon factors. We develop a model of the hyperfine and Zeeman structure that includes coupling between the 0+ and 0− components of b3Π0. We fit the spectra to obtain rotational and hyperfine coupling constants. We measure transition dipole moments associated with specific transitions by directly observing Rabi oscillations as a function of a resonant laser pulse duration. Using resonant π pulses, we prepare molecules in the electronically excited state and directly measure the spontaneous emission rate.

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References (70)

  1. R. Sawant, J. A. Blackmore, P. D. Gregory, J. Mur-Petit, D. Jaksch, J. Aldegunde, J. M. Hutson, M. R. Tarbutt, and S. L. Cornish, Ultracold polar molecules as qudits, New J. Phys. 22, 013027 (2020).
  2. A. M. Kaufman and K.-K. Ni, Quantum science with optical tweezer arrays of ultracold atoms and molecules, Nat. Phys. 17, 1324 (2021).
  3. C. Feng, H. Manetsch, V. G. Rousseau, K. R. A. Hazzard, and R. Scalettar, Quantum membrane phases in synthetic lattices of cold molecules or Rydberg atoms, Phys. Rev. A 105, 063320 (2022).
  4. C. Zhang and M. R. Tarbutt, Quantum computation in a hybrid array of molecules and Rydberg atoms, PRX Quantum 3, 030340 (2022).
  5. B. Cheng, X.-H. Deng, X. Gu, Y. He, G. Hu, P. Huang, J. Li, B.-C. Lin, D. Lu, Y. Lu, et al., Noisy intermediate-scale quantum computers, Front. Phys. 18, 21308 (2023).
  6. M. Cohen, M. Casebolt, Y. Zhang, K. R. A. Hazzard, and R. Scalettar, Classical analog of quantum models in synthetic dimensions, Phys. Rev. A 109, 013303 (2024).
  7. S. L. Cornish, M. R. Tarbutt, and K. R. A. Hazzard, Quantum computation and quantum simulation with ultracold molecules, Nat. Phys. 20, 730 (2024).
  8. A. N. Carroll, H. Hirzler, C. Miller, D. Wellnitz, S. R. Muleady, J. Lin, K. P. Zamarski, R. R. Wang, J. L. Bohn, A. M. Rey, et al., Observation of generalized t−J spin dynamics with tunable dipolar interactions, Science 388, 381 (2025).
  9. C. Miller, A. N. Carroll, J. Lin, H. Hirzler, H. Gao, H. Zhou, M. D. Lukin, and J. Ye, Two-axis twisting using Floquet-engineered XYZ spin models with polar molecules, Nature (London) 633, 332 (2024).
  10. R. V. Krems, Cold controlled chemistry, Phys. Chem. Chem. Phys. 10, 4079 (2008).
  11. 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 potassium-rubidium molecules, Science 327, 853 (2010).
  12. T. Langen, G. Valtolina, D. Wang, and J. Ye, Quantum state manipulation and cooling of ultracold molecules, Nat. Phys. 20, 702 (2024).
  13. J. Kłos, H. Li, E. Tiesinga, and S. Kotochigova, Prospects for assembling ultracold radioactive molecules from laser-cooled atoms, New J. Phys. 24, 025005 (2022).
  14. D. F. Jackson Kimball, D. Budker, T. E. Chupp, A. A. Geraci, S. Kolkowitz, J. T. Singh, and A. O. Sushkov, Probing fundamental physics with spin-based quantum sensors, Phys. Rev. A 108, 010101 (2023).
  15. D. DeMille, N. R. Hutzler, A. M. Rey, and T. Zelevinsky, Quantum sensing and metrology for fundamental physics with molecules, Nat. Phys. 20, 741 (2024).
  16. J. Huang, M. Zhuang, and C. Lee, Entanglement-enhanced quantum metrology: From standard quantum limit to Heisenberg limit, Appl. Phys. Rev. 11, 031302 (2024).
  17. B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, Observation of dipolar spin-exchange interactions with lattice-confined polar molecules, Nature (London) 501, 521 (2013).
  18. Y. Bao, S. S. Yu, L. Anderegg, E. Chae, W. Ketterle, K.-K. Ni, and J. M. Doyle, Dipolar spin-exchange and entanglement between molecules in an optical tweezer array, Science 382, 1138 (2023).
  19. C. M. Holland, Y. Lu, and L. W. Cheuk, On-demand entanglement of molecules in a reconfigurable optical tweezer array, Science 382, 1143 (2023).
  20. L. R. B. Picard, A. J. Park, G. E. Patenotte, S. Gebretsadkan, D. Wellnitz, A. M. Rey, and K.-K. Ni, Entanglement and iSWAP gate between molecular qubits, Nature (London) 637, 821 (2025).
  21. D. K. Ruttley, T. R. Hepworth, A. Guttridge, and S. L. Cornish, Long-lived entanglement of molecules in magic-wavelength optical tweezers, Nature (London) 637, 827 (2025).
  22. K. H. Leung, B. Iritani, E. Tiberi, I. Majewska, M. Borkowski, R. Moszynski, and T. Zelevinsky, Terahertz vibrational molecular clock with systematic uncertainty at the 10−14 level, Phys. Rev. X 13, 011047 (2023).
  23. J. W. Park, Z. Z. Yan, H. Loh, S. A. Will, and M. W. Zwierlein, Second-scale nuclear spin coherence time of ultracold Na23K40 molecules, Science 357, 372 (2017).
  24. K.-K. Ni, T. Rosenband, and D. D. Grimes, Dipolar exchange quantum logic gate with polar molecules, Chem. Sci. 9, 6830 (2018).
  25. P. D. Gregory, J. A. Blackmore, S. L. Bromley, J. M. Hutson, and S. L. Cornish, Robust storage qubits in ultracold polar molecules, Nat. Phys. 17, 1149 (2021).
  26. L. De Marco, G. Valtolina, K. Matsuda, W. G. Tobias, J. P. Covey, and J. Ye, A degenerate Fermi gas of polar molecules, Science 363, 853 (2019).
  27. A. Schindewolf, R. Bause, X.-Y. Chen, M. Duda, T. Karman, I. Bloch, and X.-Y. Luo, Evaporation of microwave-shielded polar molecules to quantum degeneracy, Nature (London) 607, 677 (2022).
  28. N. Bigagli, C. Warner, W. Yuan, S. Zhang, I. Stevenson, T. Karman, and S. Will, Collisionally stable gas of bosonic dipolar ground-state molecules, Nat. Phys. 19, 1579 (2023).
  29. J. Lin, G. Chen, M. Jin, Z. Shi, F. Deng, W. Zhang, G. Quéméner, T. Shi, S. Yi, and D. Wang, Microwave shielding of bosonic NaRb molecules, Phys. Rev. X 13, 031032 (2023).
  30. N. Bigagli, W. Yuan, S. Zhang, B. Bulatovic, T. Karman, I. Stevenson, and S. Will, Observation of Bose-Einstein condensation of dipolar molecules, Nature (London) 631, 289 (2024).
  31. T. Takekoshi, M. Debatin, R. Rameshan, F. Ferlaino, R. Grimm, H.-C. Nägerl, C. R. Le Sueur, J. M. Hutson, P. S. Julienne, S. Kotochigova, and E. Tiemann, Towards the production of ultracold ground-state RbCs molecules: Feshbach resonances, weakly bound states, and the coupled-channel model, Phys. Rev. A 85, 032506 (2012).
  32. M. P. Köppinger, D. J. McCarron, D. L. Jenkin, P. K. Molony, H.-W. Cho, S. L. Cornish, C. R. Le Sueur, C. L. Blackley, and J. M. Hutson, Production of optically trapped RbCs87 Feshbach molecules, Phys. Rev. A 89, 033604 (2014).
  33. 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).
  34. P. K. Molony, P. D. Gregory, Z. Ji, B. Lu, M. P. Köppinger, C. R. Le Sueur, C. L. Blackley, J. M. Hutson, and S. L. Cornish, Creation of ultracold Rb87Cs133 molecules in the rovibrational ground state, Phys. Rev. Lett. 113, 255301 (2014).
  35. H. Fahs, A. R. Allouche, M. Korek, and M. Aubert-Frécon, The theoretical spin–orbit structure of the RbCs molecule, J. Phys. B: At. Mol. Opt. Phys. 35, 1501 (2002).
  36. P. D. Gregory, L. M. Fernley, A. L. Tao, S. L. Bromley, J. Stepp, Z. Zhang, S. Kotochigova, K. R. Hazzard, and S. L. Cornish, Second-scale rotational coherence and dipolar interactions in a gas of ultracold polar molecules, Nat. Phys. 20, 415 (2024).
  37. T. R. Hepworth, D. K. Ruttley, F. von Gierke, P. D. Gregory, A. Guttridge, and S. L. Cornish, Long-lived multilevel coherences and spin-1 dynamics encoded in the rotational states of ultracold molecules, Nat. Commun. 16, 7131 (2025).
  38. Q. Guan, S. L. Cornish, and S. Kotochigova, Magic conditions for multiple rotational states of bialkali molecules in optical lattices, Phys. Rev. A 103, 043311 (2021).
  39. E. S. Shuman, J. F. Barry, and D. DeMille, Laser cooling of a diatomic molecule, Nature (London) 467, 820 (2010).
  40. D. Wang, B. Neyenhuis, M. H. G. de Miranda, K.-K. Ni, S. Ospelkaus, D. S. Jin, and J. Ye, Direct absorption imaging of ultracold polar molecules, Phys. Rev. A 81, 061404(R) (2010).
  41. C. Karam, R. Vexiau, N. Bouloufa-Maafa, O. Dulieu, M. Lepers, M. Meyer zum Alten Borgloh, S. Ospelkaus, and L. Karpa, Two-photon optical shielding of collisions between ultracold polar molecules, Phys. Rev. Res. 5, 033074 (2023).
  42. Q. Guan, M. Highman, E. J. Meier, G. R. Williams, V. Scarola, B. DeMarco, S. Kotochigova, and B. Gadway, Nondestructive dispersive imaging of rotationally excited ultracold molecules, Phys. Chem. Chem. Phys. 22, 20531 (2020).
  43. J. Kobayashi, K. Aikawa, K. Oasa, and S. Inouye, Prospects for narrow-line cooling of KRb molecules in the rovibrational ground state, Phys. Rev. A 89, 021401(R) (2014).
  44. R. Bause, M. Li, A. Schindewolf, X.-Y. Chen, M. Duda, S. Kotochigova, I. Bloch, and X.-Y. Luo, Tune-out and magic wavelengths for ground state Na23K40 molecules, Phys. Rev. Lett. 125, 023201 (2020).
  45. J. He, J. Lin, R. Vexiau, N. Bouloufa-Maafa, O. Dulieu, and D. Wang, Characterization of the lowest electronically excited-state ro-vibrational level of Na23Rb87, New J. Phys. 23, 115003 (2021).
  46. A. Yang, X. Nie, H. L. Yu, Y. Liu, V. Avalos, C. He, J. Kłos, S. Kotochigova, and K. Dieckmann, Perturbation-assisted observation of the lowest vibrational level of the b3Π0 state of ultracold LiK molecules, Phys. Chem. Chem. Phys. 28, 1705 (2026).
  47. T. Bergeman, C. E. Fellows, R. F. Gutterres, and C. Amiot, Analysis of strongly coupled electronic states in diatomic molecules: Low-lying excited states of RbCs, Phys. Rev. A 67, 050501(R) (2003).
  48. O. Docenko, M. Tamanis, R. Ferber, T. Bergeman, S. Kotochigova, A. V. Stolyarov, A. de Faria Nogueira, and C. E. Fellows, Spectroscopic data, spin-orbit functions, and revised analysis of strong perturbative interactions for the A1Σ+ and b3Π states of RbCs, Phys. Rev. A 81, 042511 (2010).
  49. A. Kruzins, K. Alps, O. Docenko, I. Klincare, M. Tamanis, R. Ferber, E. A. Pazyuk, and A. V. Stolyarov, Extended Fourier-transform spectroscopy studies and depurturbation analysis of the spin-orbit coupled A1Σ+ and b3Π states in RbCs, J. Chem. Phys. 141, 184309 (2014).
  50. A. J. Kerman, J. M. Sage, S. Sainis, T. Bergeman, and D. DeMille, Production of ultracold, polar RbCs* molecules via photoassociation, Phys. Rev. Lett. 92, 033004 (2004).
  51. M. Debatin, T. Takekoshi, R. Rameshan, L. Reichsöllner, F. Ferlaino, R. Grimm, R. Vexiau, N. Bouloufa, O. Dulieu, and H.-C. Nägerl, Molecular spectroscopy for ground-state transfer of ultracold RbCs molecules, Phys. Chem. Chem. Phys. 13, 18926 (2011).
  52. D. J. McCarron, H. W. Cho, D. L. Jenkin, M. P. Köppinger, and S. L. Cornish, Dual-species Bose-Einstein condensate of Rb87Cs133, Phys. Rev. A 84, 011603(R) (2011).
  53. J. Herbig, T. Kraemer, M. Mark, T. Weber, C. Chin, H.-C. Nägerl, and R. Grimm, Preparation of a pure molecular quantum gas, Science 301, 1510 (2003).
  54. P. K. Molony, P. D. Gregory, A. Kumar, C. R. Le Sueur, J. M. Hutson, and S. L. Cornish, Production of ultracold Rb87Cs133 in the absolute ground state: complete characterisation of the STIRAP transfer, ChemPhysChem 17, 3811 (2016).
  55. 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).
  56. P. D. Gregory, P. K. Molony, M. P. Köppinger, A. Kumar, Z. Ji, B. Lu, A. L. Marchant, and S. L. Cornish, A simple, versatile laser system for the creation of ultracold ground state molecules, New J. Phys. 17, 055006 (2015).
  57. O. Docenko, M. Tamanis, R. Ferber, H. Knöckel, and E. Tiemann, Singlet and triplet potentials of the ground-state atom pair Rb + Cs studied by Fourier-transform spectroscopy, Phys. Rev. A 83, 052519 (2011).
  58. M. Rakić, R. Beuc, N. Bouloufa-Maafa, O. Dulieu, R. Vexiau, G. Pichler, and H. Skenderović, Satellite bands of the RbCs molecule in the range of highly excited states, J. Chem. Phys. 144, 204310 (2016).
  59. R. Vexiau, D. Borsalino, M. Lepers, A. Orbán, M. Aymar, and O. Dulieu, Dynamic dipole polarizabilities of heteronuclear alkali dimers: Optical response, trapping and control of ultracold molecules, Int. Rev. Phys. Chem. 36, 709 (2017).
  60. P. K. Molony, A. Kumar, P. D. Gregory, R. Kliese, T. Puppe, C. R. Le Sueur, J. Aldegunde, J. M. Hutson, and S. L. Cornish, Measurement of the binding energy of ultracold Rb87Cs133 molecules using an offset-free optical frequency comb, Phys. Rev. A 94, 022507 (2016).
  61. S. Kotochigova (personal communication).
  62. J. Aldegunde and J. M. Hutson, Hyperfine structure of alkali-metal diatomic molecules, Phys. Rev. A 96, 042506 (2017).
  63. M. Broyer, J. Vigué, and J. Lehmann, Effective hyperfine Hamiltonian in homonuclear diatomic molecules. Application to the B state of molecular iodine, J. Phys. France 39, 591 (1978).
  64. J. Aldegunde, B. A. Rivington, P. S. Żuchowski, and J. M. Hutson, Hyperfine energy levels of Alkali-metal dimers: Ground-state polar molecules in electric and magnetic fields, Phys. Rev. A 78, 033434 (2008).
  65. A. Orbán, R. Vexiau, O. Krieglsteiner, H.-C. Nägerl, O. Dulieu, A. Crubellier, and N. Bouloufa-Maafa, Model for the hyperfine structure of electronically excited KCs molecules, Phys. Rev. A 92, 032510 (2015).
  66. A. Orbán, T. Xie, R. Vexiau, O. Dulieu, and N. Bouloufa-Maafa, Hyperfine structure of electronically-excited states of the K39Cs133 molecule, J. Phys. B: At. Mol. Opt. Phys. 52, 135101 (2019).
  67. B. Mukherjee and M. Tomza, Optical Excitation and Stabilization of Ultracold Field-Linked Tetratomic Molecules, Phys. Rev. Lett. 136, 013401 (2026).
  68. P. J. Mohr and W. D. Phillips, Dimensionless units in the SI, Metrologia 52, 40 (2014).
  69. A. Das, A. L. Tao, L. M. Fernley, F. von Gierke, P. D. Gregory, S. L. Cornish, J. M. Hutson, R. Vexiau, and O. Dulieu, Hyperfine-resolved optical spectroscopy of ultracold Rb87Cs133 molecules: The b3Π0 metastable state [dataset] (2025), https://collections.durham.ac.uk/files/r1p5547r50k.
  70. R. L. Cook and F. C. De Lucia, Application of the theory of irreducible tensor operators to molecular hyperfine structure, Am. J. Phys. 39, 1433 (1971).

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Phys. Rev. Research 8, 023005– Published 1 April, 2026
  • Received 30 October 2025
  • Accepted 4 February 2026
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