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arXiv:2410.22458 · Physical Review A

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

Jeff. Berglund, Michael Drewsen, Christiane P. Koch

Published Mar 12, 2026• 1 citation
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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, ] 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.

DOI
10.1103/7kym-lfxl

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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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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, ] 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.
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.
We investigate rotational state changes in a single collision of diatomic molecular ions, polar or apolar, with an atomic ion. Rotational state changes may occur since the angular degree of freedom of the molecular ions interacts with the electric field due to the atomic ion. Thanks to the very different time and energy scales of translational and rotational motion, we may treat the collision classically and describe only the rotations quantum mechanically. We first investigate a number of example systems numerically and then derive closed-form approximations for the rotational excitation per collision, depending on the scattering energy and the molecular parameters. These findings provide the basis for estimating the accumulated rotational excitation in sympathetic cooling of molecular ions by laser-cooled atomic ions [arXiv:2410.22458 ] which involves many single collisions.
Working with MgH+molecular ions in a linear Paul trap, we routinely cool their translational degrees of freedom by sympathetic cooling with Doppler laser cooled Mg+ions. Giving the time for the molecules to equilibrate internally to room temperature blackbody radiation, the vibrational degree of freedom is frozen out, leaving only the rotational degree of freedom to be cooled. We have implemented a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ions, using a scheme based on excitation of a single rovibrational transition. This technique is generalizable to any diatomic polar molecular ion, given an appropriate mid-infrared laser source such as a quantum cascade laser.
Stationary molecules in well-defined internal states are of broad interest in both physics and chemistry. Through high-resolution spectroscopy, fundamental physics can be tested and lead to, e.g., improved values of the electron-to-proton mass ratio [1], new boundaries on the electron electric dipole moment [2] and observation of the potential evolution of the fine structure constant over time [3]. Translationally and internally cold molecules have as well been considered promising candidates for qubits in new quantum computing senarios [4], and molecular ions could in the future likely become an excellent alternative to atomic qubits in the realization of a practical ion trap based quantum computer due to favourable internal state decoherence rates. In chemistry, state prepared molecular targets are an ideal starting point for uni-molecular reactions, including coherent control of photofragmentation through the application of various laser sources [5,6]. In cold bi-molecular reactions, where the effect of even tiny potential barriers becomes significant, experiments with state prepared molecules can yield important information on the details of the potential curves of the molecular complexes [7,8,9]. Furthermore, in order to learn more about the chemistry in interstellar clouds, astrochemists can benefit greatly from direct measurements on cold reactions in laboratories [9]. Working with MgH+ molecular ions in a linear Paul trap, we routinely cool their translational degree of freedom by sympathetic cooling with Doppler laser cooled Mg+ ions. Giving the time for the molecules to equilibrate internally to the room temperature blackbody radiation, the vibrational degree of freedom will freeze out, leaving only the rotational degree of freedom to be cooled. We report here on the implementation of a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ ions [10]. The scheme is based on excitation of a single rovibrational transition [11], and it should be generalizable to any diatomic polar molecular ion, given appropriate mid-infrared laser sources such as a quantum cascade laser are available. In recent experiments, a nearly 15-fold increase in the rotational ground-state population was obtained, with the resulting ground-state population of 36,7±1,2 %, equivalent to that of a thermal distribution at about 20 K. The obtained cooling results imply that, through this technique, cold molecular-ion experiments can now be carried out at cryogenic temperatures in room-temperature set-ups. References [1] Koelemeij, J. C. J., Roth, B., Wicht, A., Ernsting, I. and Schiller, S., Phys. Rev. Lett. 98, 173002 (2007). [2] Hudson, J. J., Sauer, B. E., Tarbutt, M. R. and Hinds, E. A., Phys. Rev. Lett. 89, 023003 (2002). [3] Hudson, E. R., Lewandowski, H. J., Sawyer, B. C. and Ye, J, Phys. Rev. Lett. 96, 143004 (2006). [4] DeMille, D, Phys. Rev. Lett. 88, 067901 (2002). [5] Rice, S. A. and Zaho, M. Optical control of molecular dynamics (Wiley, New York, 2000). [6] Shapiro, M. and Brumer, P. W. Principles of the Quantum Control of Molecular Processes (Wiley, New York, 2003). [7] Willitsch, S., Bell, M. T., Gingell, A. D. and Softley, T. P., Phys. Chem. Chem. Phys. 10, 7200 ( 2008). [8] Krems, R. V., Phys. Chem. Chem. Phys. 10, 4079 (2008). [9] Smith, I. W. M., Low temperatures and cold molecules (Imperial College Press, London, 2008). [10] Staanum, P. F., Højbjerre, K., Skyt, P.S., Hansen, A. K. and Drewsen, M., Nat. Phys. 6, 271 (2010). [11] Vogelius, I. S., Madsen, L. B. and Drewsen, M., Phys. Rev. Lett. 89, 173003 (2002).
The translational motion of molecular ions can be effectively cooled sympathetically to temperatures below 100 mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The distribution of internal rovibrational states, however, gets in thermal equilibrium with the typically much higher temperature of the environment within tens of seconds. We consider a concept for rotational cooling of such internally hot, but translationally cold, heteronuclear diatomic molecular ions. The scheme relies on a combination of optical pumping from a few specific rotational levels into a "dark state" with redistribution of rotational populations mediated by blackbody radiation.
In this Perspective, we examine the use of laser-cooled atomic ions and sympathetically cooled molecular ions in Coulomb crystals for molecular spectroscopy. Coulomb crystals are well-isolated environments that provide localization and long storage times for sensitive measurements of weak signals and cold temperatures for precise spectroscopy. Coulomb crystals of molecular and atomic ions enable the detection of single-photon molecular ion transitions at a range of wavelengths by a change in atomic ion fluorescence at visible wavelengths. We give an overview of the state of the art from action spectroscopy to quantum logic spectroscopy for a wide range of molecular transitions from rotational sublevels separated by 10 –7 cm –1 to rovibronic transitions at 25 000 cm –1 . We emphasize how this system allows for unparalleled control of the molecular ion state for precision spectroscopy with applications in astrochemistry and fundamental physics. We conclude with an outlook of the use of this control in cold molecular ion reactions.