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Vibronic coupling limits the use of high-lying electronic states in complex molecules for laser cooling

Haowen Zhou1,*, Paweł Wójcik2,*,†, Guo-Zhu Zhu1,‡, Guanming Lao1,§, Taras Khvorost3, Justin R. Caram3, Wesley C. Campbell1,4,5, Anastassia N. Alexandrova3,4, Anna I. Krylov2 et al.

Eric R. Hudson1,4,5

  • *These authors contributed equally to this work.
  • †Present address: Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, USA.
  • ‡Present address: Department of Chemistry, Fudan University, Shanghai 200438, China.
  • §Present address: Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA.
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Phys. Rev. Research 7, 043180 – Published 19 November, 2025

DOI: https://doi.org/10.1103/kw2m-hp1p

Abstract

Laser cooling of large, complex molecules is a long-standing goal, instrumental for enabling new quantum technology and precision measurements. A primary consideration for the feasibility of laser cooling, which determines the efficiency and technical requirements of the process, is the number of excited-state decay pathways leading to vibrational excitations. Therefore, the assessment of the laser-cooling potential of a molecule begins with estimate of the vibrational branching ratios of the first few electronic excited states theoretically to find the optimum cooling scheme. Such calculations, typically done within the Born-Oppenheimer and harmonic approximations, have suggested that one leading candidate for large, polyatomic molecule laser cooling, alkaline earth phenoxides, can most efficiently be laser cooled via the third electronically excited (C̃) state. Here, we report the first detailed spectroscopic characterization of the C̃ state in CaOPh and SrOPh. We find that nonadiabatic couplings between the Ã, B̃, and C̃ states lead to substantial mixing, giving rise to vibronic states that enable additional decay pathways. Based on the intensity ratio of these extra decay channels, we estimate a nonadiabatic coupling strength of ∼0.1cm−1. While this coupling strength is small, the large density of vibrational states available at photonic energy scales in a polyatomic molecule leads to significant mixing. Only the lowest excited state à is exempt from this coupling because it is highly separated from the ground state. Thus, this result is expected to be general for large molecules and implies that only the lowest electronic excited state should be considered when judging the suitability of a molecule for laser cooling.

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References (72)

  1. P. Yu, L. W. Cheuk, I. Kozyryev, and J. M. Doyle, A scalable quantum computing platform using symmetric-top molecules, New J. Phys. 21, 093049 (2019).
  2. W. C. Campbell and E. R. Hudson, Dipole-phonon quantum logic with trapped polar molecular ions, Phys. Rev. Lett. 125, 120501 (2020).
  3. E. R. Hudson and W. C. Campbell, Laserless quantum gates for electric dipoles in thermal motion, Phys. Rev. A 104, 042605 (2021).
  4. C. M. Holland, Y. Lu, and L. W. Cheuk, On-demand entanglement of molecules in a reconfigurable optical tweezer array, Science 382, 1143 (2023).
  5. 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).
  6. S. L. Cornish, M. R. Tarbutt, and K. R. A. Hazzard, Quantum computation and quantum simulation with ultracold molecules, Nat. Phys. 20, 730 (2024).
  7. B. L. Augenbraun, J. M. Doyle, T. Zelevinsky, and I. Kozyryev, Molecular asymmetry and optical cycling: Laser cooling asymmetric top molecules, Phys. Rev. X 10, 031022 (2020).
  8. B. L. Augenbraun et al., Laser-cooled polyatomic molecules for improved electron electric dipole moment searches, New J. Phys. 22, 022003 (2020).
  9. N. R. Hutzler, Polyatomic molecules as quantum sensors for fundamental physics, Quantum Sci. Technol. 5, 044011 (2020).
  10. L. Anderegg et al., Quantum control of trapped polyatomic molecules for eEDM searches, Science 382, 665 (2023).
  11. N. Balakrishnan, Perspective: Ultracold molecules and the dawn of cold controlled chemistry, J. Chem. Phys. 145, 150901 (2016).
  12. P. Puri et al., Synthesis of mixed hypermetallic oxide BaOCa+ from laser-cooled reagents in an atom-ion hybrid trap, Science 357, 1370 (2017).
  13. M.-G. Hu et al., Direct observation of bimolecular reactions of ultracold KRb molecules, Science 366, 1111 (2019).
  14. P. D. Gregory et al., Molecule–molecule and atom–molecule collisions with ultracold RbCs molecules, New J. Phys. 23, 125004 (2021).
  15. X.-Y. Chen et al., Ultracold field-linked tetratomic molecules, Nature (London) 626, 283 (2024).
  16. W. D. Phillips, Nobel lecture: Laser cooling and trapping of neutral atoms, Rev. Mod. Phys. 70, 721 (1998).
  17. M. D. Rosa, Laser-cooling molecules: Concept, candidates, and supporting hyperfine-resolved measurements of rotational lines in the A-X(0,0) band of CaH, Eur. Phys. J. D 31, 395 (2004).
  18. N. Fitch and M. Tarbutt, Laser-cooled molecules, Advances in Atomic, Molecular, and Optical Physics (Elsevier, Amsterdam, Netherlands, 2021), Vol. 70, pp. 157–262.
  19. E. S. Shuman, J. F. Barry, and D. Demille, Laser cooling of a diatomic molecule, Nature (London) 467, 820 (2010).
  20. L. Anderegg et al., Radio frequency magneto-optical trapping of CaF with high density, Phys. Rev. Lett. 119, 103201 (2017).
  21. A. L. Collopy et al., 3D magneto-optical trap of yttrium monoxide, Phys. Rev. Lett. 121, 213201 (2018).
  22. L. Baum et al., 1D magneto-optical trap of polyatomic molecules, Phys. Rev. Lett. 124, 133201 (2020).
  23. I. Kozyryev et al., Sisyphus laser cooling of a polyatomic molecule, Phys. Rev. Lett. 118, 173201 (2017).
  24. D. Mitra et al., Direct laser cooling of a symmetric top molecule, Science 369, 1366 (2020).
  25. B. L. Augenbraun et al., Direct laser cooling of polyatomic molecules, Advances In Atomic, Molecular, and Optical Physics (Elsevier, Amsterdam, Netherlands, 2023), Vol. 72, pp. 89–182.
  26. I. Kozyryev, L. Baum, K. Matsuda, and J. M. Doyle, Proposal for laser cooling of complex polyatomic molecules, ChemPhysChem 17, 3641 (2016).
  27. T. A. Isaev and R. Berger, Polyatomic candidates for cooling of molecules with lasers from simple theoretical concepts, Phys. Rev. Lett. 116, 063006 (2016).
  28. J. Kłos and S. Kotochigova, Prospects for laser cooling of polyatomic molecules with increasing complexity, Phys. Rev. Res. 2, 013384 (2020).
  29. H. Zhou, T. Khvorost, A. N. Alexandrova, and J. R. Caram, Vibronic engineering for quantum functional groups, Acc. Chem. Res. 58, 1181 (2025).
  30. G.-Z. Zhu et al., Functionalizing aromatic compounds with optical cycling centers, Nat. Chem. 14, 995 (2022).
  31. M. V. Ivanov, F. H. Bangerter, P. Wójcik, and A. Krylov, Towards ultracold organic chemistry: Prospects of laser cooling large organic molecules, J. Phys. Chem. Lett. 11, 6670 (2020).
  32. C. E. Dickerson et al., Optical cycling functionalization of arenes, J. Phys. Chem. Lett. 12, 3989 (2021).
  33. D. Mitra et al., Pathway toward optical cycling and laser cooling of functionalized arenes, J. Phys. Chem. Lett. 13, 7029 (2022).
  34. G. Lao et al., Bottom-up approach to scalable growth of molecules capable of optical cycling, arXiv:2411.03199.
  35. H. Guo et al., Surface chemical trapping of optical cycling centers, Phys. Chem. Chem. Phys. 23, 211 (2021).
  36. C. E. Dickerson et al., Franck-Condon tuning of optical cycling centers by organic functionalization, Phys. Rev. Lett. 126, 123002 (2021).
  37. N. B. Vilas et al., Magneto-optical trapping and sub-Doppler cooling of a polyatomic molecule, Nature (London) 606, 70 (2022).
  38. S. F. Vázquez-Carson, Q. Sun, J. Dai, D. Mitra, and T. Zelevinsky, Direct laser cooling of calcium monohydride molecules, New J. Phys. 24, 083006 (2022).
  39. M. Kasha, Characterization of electronic transitions in complex molecules, Discuss. Faraday Soc. 9, 14 (1950).
  40. G.-Z. Zhu et al., Extending the large molecule limit: The role of Fermi resonance in developing a quantum functional group, J. Phys. Chem. Lett. 15, 590 (2024).
  41. A. Ivanov, Y. Rozhdestvensky, and E. Perlin, Vibronic model of laser cooling with stimulated Raman adiabatic passage pumping for Yb3+-ion-doped crystals, J. Opt. Soc. Am. B 33, 1564 (2016).
  42. H. Köppel, W. Domcke, and L. Cederbaum, Multimode molecular dynamics beyond the Born–Oppenheimer approximation, Adv. Chem. Phys. 57, 59 (1984).
  43. W. Domcke, H. Köppel, and L. S. Cederbaum, Spectroscopic effects of conical intersections of molecular potential energy surfaces, Mol. Phys. 43, 851 (1981).
  44. H. Köppel, W. Domcke, and L. S. Cederbaum, The Multi-Mode Vibronic-Coupling Approach (World Scientific, Singapore, 2004), Chap. 7, pp. 323–367.
  45. J. F. Stanton and R. J. Bartlett, The equation of motion coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties, J. Chem. Phys. 98, 7029 (1993).
  46. M. Nooijen and R. J. Bartlett, Equation of motion coupled cluster method for electron attachment, J. Chem. Phys. 102, 3629 (1995).
  47. R. Bartlett and M. Musiał, Coupled-cluster theory in quantum mechanics, Rev. Mod. Phys. 79, 291 (2007).
  48. A. I. Krylov, Equation-of-motion coupled-cluster methods for open-shell and electronically excited species: The hitchhiker’s guide to Fock space, Annu. Rev. Phys. Chem. 59, 433 (2008).
  49. A. I. Krylov, The quantum chemistry of open-shell species, in Reviews in Computational Chemistry, edited by A. L. Parrill and K. B. Lipkowitz (Wiley, Hoboken, NJ, 2017), Vol. 30, pp. 151–224.
  50. H. Köppel, M. Döscher, I. Baldea, H.-D. Meyer, and P. G. Szalay, Multistate vibronic interactions in the benzene radical cation. II. Quantum dynamical simulations, J. Chem. Phys. 117, 2657 (2002).
  51. J. F. Stanton, On the vibronic level structure in the NO3 radical. I. The ground electronic state, J. Chem. Phys. 126, 134309 (2007).
  52. P. Wójcik, H. Reisler, P. G. Szalay, A. I. Krylov, and J. F. Stanton, Vibronic coupling effects in the photoelectron spectrum of ozone: A coupled-cluster approach, J. Phys. Chem. A 128, 10957 (2024).
  53. G. Lao et al., Laser spectroscopy of aromatic molecules with optical cycling centers: Strontium(I) phenoxides, J. Phys. Chem. Lett. 13, 11029 (2022).
  54. H. Lefebvre-Brion and R. W. Field, The Spectra and Dynamics of Diatomic Molecules (Elsevier, Amsterdam, Netherlands, 2004).
  55. H. Zhou et al., Vibronic coupling limits the use of high-lying electronic states in complex molecules for laser cooling, Zenodo, https://zenodo.org/records/16897009.
  56. T. Ichino, J. Gauss, and J. F. Stanton, Quasidiabatic states described by coupled-cluster theory, J. Chem. Phys. 130, 174105 (2009).
  57. J. Stanton and J. Gauss, A simple correction to final state energies of doublet radicals described by equation-of-motion coupled cluster theory in the singles and doubles approximation, Theor. Chim. Acta 93, 303 (1996).
  58. J. Stanton, J. Gauss, M. Harding, and P. Szalay, CFOUR, with contributions from, A. A. Auer, R. J. Bartlett, U. Benedikt, C. Berger, D. E. Bernholdt, Y. J. Bomble, L. Cheng, O. Christiansen, M. Heckert, O. Heun, C. Huber, T.-C. Jagau, D. Jonsson, J. Jusélius, K. Klein, W. J. Lauderdale, F. Lipparini, D. A. Matthews, T. Metzroth, L. A. Mück, D. P. O’Neill, D. R. Price, E. Prochnow, C. Puzzarini, K. Ruud, F. Schiffmann, W. Schwalbach, C. Simmons, S. Stopkowicz, A. Tajti, J. Vázquez, F. Wang, J. D. Watts; and the integral packages MOLECULE (J. Almlöf and P. R. Taylor), PROPS (P. R. Taylor), ABACUS (T. Helgaker, H.J.Aa. Jensen, P. Jørgensen, and J. Olsen), and ECP routines by A. V. Mitin and C. van Wüllen. For the current version, see http://www.cfour.de.
  59. D. A. Matthews et al., Coupled-cluster techniques for computational chemistry: The CFOUR program package, J. Chem. Phys. 152, 214108 (2020).
  60. A. I. Krylov and P. M. W. Gill, Q-Chem: An engine for innovation, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 3, 317 (2013).
  61. E. Epifanovsky et al., Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package, J. Chem. Phys. 155, 084801 (2021).
  62. K. Sharma, O. A. Vasilyev, T. A. Miller, and J. F. Stanton, Molecules with spin and vibronic coupling effects: A computational perspective, J. Phys.: Conf. Ser. 2769, 012002 (2024).
  63. E. T. Mengesha et al., Branching ratios, radiative lifetimes, and transition dipole moments for YbOH, J. Phys. Chem. A 124, 3135 (2020).
  64. C. Zhang et al., Accurate prediction and measurement of vibronic branching ratios for laser cooling linear polyatomic molecules, J. Chem. Phys. 155, 091101 (2021).
  65. Z. Lasner, A. Lunstad, C. Zhang, L. Cheng, and J. M. Doyle, Vibronic branching ratios for nearly closed rapid photon cycling of SrOH, Phys. Rev. A 106, L020801 (2022).
  66. C. Zhang, N. R. Hutzler, and L. Cheng, Intensity-borrowing mechanisms pertinent to laser cooling of linear polyatomic molecules, J. Chem. Theory Comput. 19, 4136 (2023).
  67. A. Frenett, Z. Lasner, L. Cheng, and J. M. Doyle, Vibrational branching fractions for laser cooling of nonlinear strontium-containing molecules, Phys. Rev. A 110, 022811 (2024).
  68. J. R. Barker et al., MultiWell Software Suite; University of Michigan, Ann Arbor, Michigan, USA, 2023; https://multiwell.engin.umich.edu/.
  69. J. R. Barker, Multiple-well, multiple-path unimolecular reaction systems. I. MultiWell computer program suite, Int. J. Chem. Kinet. 33, 232 (2001).
  70. J. R. Barker, Energy transfer in master equation simulations: A new approach, Int. J. Chem. Kinet. 41, 748 (2009).
  71. T. Beyer and D. Swinehart, Algorithm 448: Number of multiply-restricted partitions, Commun. ACM 16, 379 (1973).
  72. S. E. Stein and B. Rabinovitch, Accurate evaluation of internal energy level sums and densities including anharmonic oscillators and hindered rotors, J. Chem. Phys. 58, 2438 (1973).

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Phys. Rev. Research 7, 043180– Published 19 November, 2025
  • Received 18 August 2025
  • Accepted 22 October 2025
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