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Rotational excitation in sympathetic cooling of diatomic molecular ions by laser-cooled atomic ions

J. Martin Berglund1,2, Michael Drewsen3, and Christiane P. Koch1,4,*

  • *Contact author: christiane.koch@fu-berlin.de
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Phys. Rev. A 113, 042817 – Published 16 April, 2026

DOI: https://doi.org/10.1103/7kym-lfxl

Abstract

Sympathetic cooling of molecular ions through the Coulomb interaction with laser-cooled atomic ions is an efficient tool to prepare translationally cold molecules without, ideally, affecting the internal state of the molecular ions. However, the electric field due to the Coulomb interaction may induce rotational transitions that change the purity of initially quantum state prepared molecules. Here, we use estimates of rotational state changes in single collisions of diatomic ions with atomic ions [J. M. Berglund, M. Drewsen, and C. P. Koch, Phys. Rev. A 113, 042816 (2026)] to determine the overall rotational excitation accumulated over the sympathetic cooling. Considering two different experimental scenarios, that of a molecular ion cotrapped with a single atomic ion and a molecular ion immersed in a Coulomb crystal of atomic ions, we also estimate the cooling time.

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Rotational state changes in collisions of diatomic molecular ions with atomic ions

J. Martin Berglund, Michael Drewsen, and Christiane P. Koch
Phys. Rev. A 113, 042816 (2026)

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References (48)

  1. K. Mølhave and M. Drewsen, Formation of translationally cold MgH+ and MgD+ molecules in an ion trap, Phys. Rev. A 62, 011401(R) (2000).
  2. P. Bowe, L. Hornekær, C. Brodersen, M. Drewsen, J. S. Hangst, and J. P. Schiffer, Sympathetic crystallization of trapped ions, Phys. Rev. Lett. 82, 2071 (1999).
  3. J. C. J. Koelemeij, B. Roth, A. Wicht, I. Ernsting, and S. Schiller, Vibrational spectroscopy of HD+ with 2-ppb accuracy, Phys. Rev. Lett. 98, 173002 (2007).
  4. P. F. Staanum, K. Højbjerre, R. Wester, and M. Drewsen, Probing isotope effects in chemical reactions using single ions, Phys. Rev. Lett. 100, 243003 (2008).
  5. S. Willitsch, M. T. Bell, A. D. Gingell, S. R. Procter, and T. P. Softley, Cold reactive collisions between laser-cooled ions and velocity-selected neutral molecules, Phys. Rev. Lett. 100, 043203 (2008).
  6. A. K. Hansen, M. A. Sørensen, P. F. Staanum, and M. Drewsen, Single-ion recycling reactions, Angew. Chem., Int. Ed. 51, 7960 (2012).
  7. P. Blythe, B. Roth, U. Fröhlich, H. Wenz, and S. Schiller, Production of ultracold trapped molecular hydrogen ions, Phys. Rev. Lett. 95, 183002 (2005).
  8. X. Tong, A. H. Winney, and S. Willitsch, Sympathetic cooling of molecular ions in selected rotational and vibrational states produced by threshold photoionization, Phys. Rev. Lett. 105, 143001 (2010).
  9. A. Ostendorf, C. B. Zhang, M. A. Wilson, D. Offenberg, B. Roth, and S. Schiller, Sympathetic cooling of complex molecular ions to millikelvin temperatures, Phys. Rev. Lett. 97, 243005 (2006).
  10. K. Højbjerre, D. Offenberg, C. Z. Bisgaard, H. Stapelfeldt, P. F. Staanum, A. Mortensen, and M. Drewsen, Consecutive photodissociation of a single complex molecular ion, Phys. Rev. A 77, 030702(R) (2008).
  11. A. Calvin, S. Eierman, Z. Peng, M. Brzeczek, S. Kresch, E. Lane, L. Satterthwaite, and D. Patterson, Nondestructive inelastic recoil spectroscopy of a single molecular ion: A versatile tool toward precision action spectroscopy, Phys. Rev. A 108, 062819 (2023).
  12. M. Shi, P. F. Herskind, M. Drewsen, and I. L. Chuang, Microwave quantum logic spectroscopy and control of molecular ions, New J. Phys. 15, 113019 (2013).
  13. M. Sinhal and S. Willitsch, Molecular-ion quantum technologies, in Photonic Quantum Technologies (Wiley & Sons, Hoboken, NJ, 2023), Chap. 13, pp. 305–332.
  14. B. J. Furey, Z. Wu, M. Isaza-Monsalve, S. Walser, E. Mattivi, R. Nardi, and P. Schindler, Strategies for implementing quantum error correction in molecular rotation, Quantum 8, 1578 (2024).
  15. S. Schiller and V. Korobov, Tests of time independence of the electron and nuclear masses with ultracold molecules, Phys. Rev. A 71, 032505 (2005).
  16. M. S. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A. Derevianko, and C. W. Clark, Search for new physics with atoms and molecules, Rev. Mod. Phys. 90, 025008 (2018).
  17. N. R. Hutzler, Polyatomic molecules as quantum sensors for fundamental physics, Quantum Sci. Technol. 5, 044011 (2020).
  18. I. Erez, E. R. Wallach, and Y. Shagam, Simultaneous enantiomer-resolved Ramsey spectroscopy scheme for chiral molecules, Phys. Rev. X 13, 041025 (2023).
  19. Edited by O. Dulieu and A. Osterwalder, Cold Chemistry: Molecular Scattering and Reactivity Near Absolute Zeroed (The Royal Society of Chemistry, London, UK, 2018).
  20. M. Deiß, S. Willitsch, and J. Hecker Denschlag, Cold trapped molecular ions and hybrid platforms for ions and neutral particles, Nat. Phys. 20, 713 (2024).
  21. A. Calvin, S. Kresch, M. Brzeczek, E. Lane, L. Satterthwaite, D. Hawkins, and D. Patterson, Rotationally resolved spectroscopy of a single polyatomic molecule, Phys. Rev. Lett. 134, 153002 (2025).
  22. D. I. Schuster, L. S. Bishop, I. L. Chuang, D. DeMille, and R. J. Schoelkopf, Cavity QED in a molecular ion trap, Phys. Rev. A 83, 012311 (2011).
  23. Y. Lin, D. R. Leibrandt, D. Leibfried, and C.-w. Chou, Quantum entanglement between an atom and a molecule, Nature (London) 581, 273 (2020).
  24. C.-w. Chou, C. Kurz, D. B. Hume, P. N. Plessow, D. R. Leibrandt, and D. Leibfried, Preparation and coherent manipulation of pure quantum states of a single molecular ion, Nature (London) 545, 203 (2017).
  25. M. Sinhal, Z. Meir, K. Najafian, G. Hegi, and S. Willitsch, Quantum-nondemolition state detection and spectroscopy of single trapped molecules, Science 367, 1213 (2020).
  26. P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, Spectroscopy using quantum logic, Science 309, 749 (2005).
  27. F. Wolf, Y. Wan, J. C. Heip, F. Gebert, C. Shi, and P. O. Schmidt, Non-destructive state detection for quantum logic spectroscopy of molecular ions, Nature (London) 530, 457 (2016).
  28. D. Holzapfel, F. Schmid, N. Schwegler, O. Stadler, M. Stadler, A. Ferk, J. P. Home, and D. Kienzler, Quantum control of a single H2+ molecular ion, Phys. Rev. X 15, 031009 (2025).
  29. Y. Wan, F. Gebert, F. Wolf, and P. O. Schmidt, Efficient sympathetic motional-ground-state cooling of a molecular ion, Phys. Rev. A 91, 043425 (2015).
  30. R. Rugango, J. E. Goeders, T. H. Dixon, J. M. Gray, N. B. Khanyile, G. Shu, R. J. Clark, and K. R. Brown, Sympathetic cooling of molecular ion motion to the ground state, New J. Phys. 17, 035009 (2015).
  31. G. Poulsen, Sideband cooling of atomic and molecular ions, Ph.D. thesis, Department of Physics and Astronomy, Aarhus University, 2011.
  32. I. S. Vogelius, L. B. Madsen, and M. Drewsen, Blackbody-radiation–assisted laser cooling of molecular ions, Phys. Rev. Lett. 89, 173003 (2002).
  33. P. F. Staanum, K. Højbjerre, P. S. Skyt, A. K. Hansen, and M. Drewsen, Rotational laser cooling of vibrationally and translationally cold molecular ions, Nat. Phys. 6, 271 (2010).
  34. T. Schneider, B. Roth, H. Duncker, I. Ernsting, and S. Schiller, All-optical preparation of molecular ions in the rovibrational ground state, Nat. Phys. 6, 275 (2010).
  35. N. Deb, B. R. Heazlewood, M. T. Bell, and T. P. Softley, Blackbody-mediated rotational laser cooling schemes in MgH+, DCl+, HCl+, LiH and CsH, Phys. Chem. Chem. Phys. 15, 14270 (2013).
  36. A. K. Hansen, O. O. Versolato, L. Kłosowski, S. B. Kristensen, A. Gingell, M. Schwarz, A. Windberger, J. Ullrich, J. R. C. López-Urrutia, and M. Drewsen, Efficient rotational cooling of Coulomb-crystallized molecular ions by a helium buffer gas, Nature (London) 508, 76 (2014).
  37. A. Gardner, T. Softley, and M. Keller, Multi-photon ionisation spectroscopy for rotational state preparation of N2+, Sci. Rep. 9, 506 (2019).
  38. H. J. Kim, F. Schmid, D. Holzapfel, and D. Kienzler, State-selective Ionization and trapping of single H2+ Ions with (2 + 1) multiphoton Ionization, arXiv:2509.03625.
  39. M. H. Stockett, J. Houmøller, K. Støchkel, A. Svendsen, and S. Brøndsted Nielsen, A cylindrical quadrupole ion trap in combination with an electrospray ion source for gas-phase luminescence and absorption spectroscopy, Rev. Sci. Instrum. 87, 053103 (2016).
  40. J. M. Berglund, M. Drewsen, and C. P. Koch, preceding paper, Rotational state changes in collisions of diatomic molecular ions with atomic ions, Phys. Rev. A 113, 042816 (2026).
  41. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1980).
  42. B. R. Heazlewood and T. P. Softley, Low-temperature kinetics and dynamics with coulomb crystals, Annu. Rev. Phys. Chem. 66, 475 (2015).
  43. M. Bussmann, U. Schramm, D. Habs, V. Kolhinen, and J. Szerypo, Stopping highly charged ions in a laser-cooled one component plasma of ions, Int. J. Mass Spectrom. 251, 179 (2006).
  44. M. Germann, X. Tong, and S. Willitsch, Observation of electric-dipole-forbidden infrared transitions in cold molecular ions, Nat. Phys. 10, 820 (2014).
  45. M. Germann and S. Willitsch, Fine- and hyperfine-structure effects in molecular photoionization. I. General theory and direct photoionization, J. Chem. Phys. 145, 044314 (2016).
  46. M. Germann and S. Willitsch, Fine- and hyperfine-structure effects in molecular photoionization. II. Resonance-enhanced multiphoton ionization and hyperfine-selective generation of molecular cations, J. Chem. Phys. 145, 044315 (2016).
  47. A. Hashemloo and C. M. Dion, Rotational dynamics of a diatomic molecular ion in a Paul trap, J. Chem. Phys. 143, 204308 (2015).
  48. A. Hashemloo, C. M. Dion, and G. Rahali, Wave packet dynamics of an atomic ion in a Paul trap, Int. J. Mod. Phys. C 27, 1650014 (2016).

Outline

Information

Phys. Rev. A 113, 042817– Published 16 April, 2026
  • Received 12 January 2026
  • Accepted 12 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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