Abstract
Energy transfer between different mechanical degrees of freedom in atom–molecule collisions has been studied and largely understood. However, systems involving spins remain less explored. In this study, we directly observed energy transfer from atomic hyperfine to molecular rotation in the 87Rb (\(| {F}_{a},{M}_{{F}_{a}}\rangle =| 2,2\rangle\)) + 40K87Rb (X1Σ+, rotational state N = 0) ⟶ Rb (\(| 1,1\rangle\)) + KRb (N = 0, 1, 2) collision with state-to-state precision. We also performed quantum scattering calculations that rigorously included the coupling between spin and rotational degrees of freedom at short range under the assumption of rigid-rotor KRb monomers moving along a single potential energy surface. The calculated product rotational state distribution deviates from the observations even after extensive tuning of the atom–molecule potential energy surface. In addition, our ab initio calculations indicate that spin–rotation coupling is enhanced close to a conical intersection that is energetically accessible at short range. This, together with the deviation, suggests that vibrational degrees of freedom and conical intersections play an important part in the coupling. Our observations confirm that spin is coupled to mechanical rotation at short range and establish a benchmark for future theoretical studies.
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The data supporting the findings of this study are available from the corresponding authors on request. Experimental data and related processing codes are also accessible at Harvard Dataverse via https://doi.org/10.7910/DVN/O24MN4 (ref. 54).
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Acknowledgements
We thank M. Frye, Y. Liu, J. Zhang, Z. Li and A. Houwman for helpful discussions. The experimental team (Y.-X.L., L.Z., J.L., M.C.B. and K.-K.N.) was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (award no. DE-SC0024087; molecule state detection), the Center for Ultracold Atoms (an NSF Physics Frontiers Center, PHY-2317134; atom state detection) and AFOSR DURIP FA9550-23-1-0122 (instrument upgrade). The Warsaw team (M.G., H.L. and M.T.) acknowledges the European Union (ERC, 101042989, QuantMol) and the PL-Grid Infrastructure (grant no. PLG/2023/016115). T.V.T. gratefully acknowledges support from the NSF CAREER program (grant no. PHY-2045681). J.L.B. acknowledges support from the JILA Physics Frontier Center (PHY-2317149).
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Y.-X.L., L.Z., J.L., M.C.B. and K.-K.N. carried out the experimental work and data analysis. T.V.T. carried out the coupled-channel calculations. M.G., H.L. and M.T. performed the ab initio calculations of the Rb + KRb interactions. J.L.B. developed the statistical model of the KRb branching ratio. All authors contributed to the interpretation of the results and writing of the paper.
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Extended data
Extended Data Fig. 1 Light shift and hyperfine structure observed in the R(0) transition.
(a) Pulsed 532 nm light induced light shift in the R(0) transition. The dark blue solid circles represent the R(0) transition with an overlapping 666 nm pulse and 532 nm pulse. The light blue open circles represent the R(0) transition without overlapping 666 nm and 532 nm pulses. The solid lines are fittings to Lorentzian lineshapes. The insets are the corresponding REMPI pulse timing diagrams. The data were collected using 5 averages. (b) Depletion spectroscopy of N = 0 KRb molecules from absorption imaging near R(0) transitions. The spectrum shows hyperfine structure of the N = 1 level in the electronically excited state. The data points represent the mean value, normalized to the maximum molecule number. All error bars in this figure represent the shot noise.
Extended Data Fig. 2 Rb atom number dependence of KRb ion counts.
KRb ion counts were measured with the 666 nm laser resonant with the Q(2) (circles), Q(1) (triangles) and R(0) (squares) transitions as a function of the initial \(| 2,2\rangle\) Rb atom number, which was controlled by varying the duration of the microwave ARP pulse. To account for imperfections in the dark mask that give rise to signal from \(| 1,1\rangle\) atoms in the reactant cloud, the same measurements were performed without a microwave ARP pulse to establish a background. The results with background subtraction are shown here. For each point, the X-axis values and error bars indicate the mean and standard deviation of relative atom number of the 5 measurements, while Y-axis values and error bars represent the mean of 5 measurements and shot noise. Solid lines are linear fits to the data.
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Liu, YX., Zhu, L., Luke, J. et al. Hyperfine-to-rotational energy transfer in ultracold atom–molecule collisions of Rb and KRb. Nat. Chem. 17, 688–694 (2025). https://doi.org/10.1038/s41557-025-01778-z
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DOI: https://doi.org/10.1038/s41557-025-01778-z
