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arXiv:2510.16203 · Computer Physics Communications

Numerical modeling of laser cooling in molecules: From simple diatomics to polyatomics and radioactive species

Felix Kogel, Tatsam Garg, Phillip Groß, Lukas Leczek, Marian Rockenhäuser, Neil Shah, Jakob Weiß, Andreas Schindewolf, Tim Langen

Published May 22, 2026• 1 citation
arXivHTMLPDF

Abstract

Optical Bloch equations and rate equations serve as powerful tools to model light-matter interactions from textbook-like two-level atoms to the complex internal dynamics of molecules. A particular challenge in this context is posed by molecular laser cooling, where many dozens or hundreds of levels need to be taken into account for a comprehensive modeling. Here, we present MoleCool, a numerically efficient Python toolbox to implement and solve the corresponding differential equation systems. We illustrate both the capabilities of the toolbox and some of the intricacies of molecular laser cooling by educational examples, which range from simple Rabi oscillations to spontaneous and coherent cooling schemes for various currently studied or considered molecular species. This includes, in particular, a comprehensive modeling of laser cooling dynamics with full hyperfine structure resolution in radioactive radium monofluoride (RaF), as well as studies of other complex species such as barium monofluoride (BaF) and ytterbium monohydroxide (YbOH).

DOI
10.1016/j.cpc.2026.110235

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Optical Bloch equations and rate equations serve as powerful tools to model light-matter interactions from textbook-like two-level atoms to the complex internal dynamics of molecules. A particular challenge in this context is posed by molecular laser cooling, where many dozens or hundreds of levels need to be taken into account for a comprehensive modeling. Here, we present MoleCool, a numerically efficient Python toolbox to implement and solve the corresponding differential equation systems. We illustrate both the capabilities of the toolbox and some of the intricacies of molecular laser cooling by educational examples, which range from simple Rabi oscillations to spontaneous and coherent cooling schemes for various currently studied or considered molecular species. This includes, in particular, a comprehensive modeling of laser cooling dynamics with full hyperfine structure resolution in radioactive radium monofluoride (RaF), as well as studies of other complex species such as barium monofluoride (BaF) and ytterbium monohydroxide (YbOH).
Molecules controlled at the single-quantum-state level offer wide-ranging applications spanning many of the frontiers of modern physics. Within the past decade, simple diatomic molecules have been brought under full quantum control both via assembly from pre-cooled atoms and by direct laser cooling. Polyatomic molecules\footnote{Molecules that contain three or more atoms.} have attracted focus as novel quantum resources providing distinct advantages (and challenges) compared to both atoms and diatomic molecules. For example, nearly all polyatomic molecules have long-lived states that can be fully polarized at low applied electric fields. These and other features generic to polyatomic molecules can be applied to quantum simulation, quantum chemistry, and tests of fundamental physics beyond the Standard Model. While these structural features of polyatomic molecules are highly promising for applications, they complicate the process of bringing molecules under full quantum control. In this thesis, we describe a series of experimental and theoretical advances toward the production of ultracold complex polyatomic molecules. We demonstrate the first laser cooling of the polyatomic radical ytterbium monohydroxide (YbOH), a promising candidate to search for particles and interactions beyond the Standard Model of particle physics. We develop a novel deceleration technique (``Zeeman-Sisyphus deceleration") capable of slowing molecular beams to trappable velocities while scattering fewer than 10 optical photons. This deceleration method is demonstrated using CaOH molecules, a lighter analog of YbOH. In order to determine a viable pathway to full three-dimensional cooling and trapping of YbOH, we develop a spectroscopic technique to measure vibrational branching ratios with relative intensity sensitivity around 1 part in 10510^5105, approximately two orders of magnitude beyond the previous state of the art. We also perform the first spectroscopic observations and characterizations of the related molecule ytterbium monomethoxide, YbOCH3_33​, a promising species to probe beyond-the-Standard-Model physics. In addition, we show theoretically that an entire class of asymmetric top molecules can be laser cooled using essentially the same techniques used for much simpler species. Measurements of the vibrational branching ratios for a few prototypical asymmetric to molecules (CaSH and CaNH2_22​) are presented to confirm these predictions.
Abstract An important effort is currently underway to extend optical cycling and laser cooling to more molecular species. Significant challenges arise in particular when multiple nuclear spins give rise to complex, resolved hyperfine spectra, as is the case for several molecular species relevant to precision tests of fundamental symmetries. We provide a detailed introduction to the use of optical spectra generated via serrodyne waveforms to address this complexity. We discuss our experimental implementation of these serrodynes, characterize their properties, and outline procedures to find optimized sideband configurations that generate strong laser cooling forces. We demonstrate the application of these techniques to barium monofluoride molecules and explore their prospects for the cooling of other species relevant to the study of fundamental physics.
Abstract Recently, a few diatomic and polyatomic molecules have been identified as prospective systems for Doppler/Sisyphus cooling. Doppler/Sisyphus cooling allows us to decrease the kinetic energy of molecules down to μ K temperatures with high efficiency and allows their capture in molecular traps, including magneto-optical traps. Trapped molecules can be used for creating molecular fountains and/or performing controlled chemical reactions, high-precision spectra measurements, and a wealth of other applications. Polyatomic molecules with heavy nuclei are of considerable interest for the ‘new physics’ search outside of the Standard Model and other applications including cold chemistry and photochemistry, quantum informatics, etc. Here, we focus on the radium monohydroxide molecule (RaOH), which is on the one hand amenable to laser cooling and on the other hand opens excellent possibilities for  -odd and  ,  -odd effects research. At present, RaOH is the heaviest polyatomic molecule proposed for direct cooling with lasers.
We theoretically investigate the laser cooling of fermionic barium monofluoride (137BaF) molecules, which are promising candidates for precision studies of weak parity violation and nuclear anapole moments. This molecular species features two nuclear spins, resulting in a hyperfine structure that is considerably more complicated than the one found in the usual laser-cooled diatomics. We use optical Bloch equations and rate equations to show that optical cycling, sub-Doppler cooling and bichromatic forces can all be realized under realistically achievable experimental conditions.
To laser-cool a species, a closed (or nearly closed) cycle is required to dissipate translational energy through many directed laser-photon absorption and subsequent randomly-directed spontaneous emission events. Many atoms lend themselves to such a closed-loop cooling cycle. Attaining laser-cooled molecular species is challenging because of their inherently complex internal structure, yet laser-cooling molecules could lead to studies in interesting chemical dynamics among other applications. Typically, laser-cooled atoms are assembled into molecules through photoassociation or Feschbach resonance. CaH is one of a few molecules whose internal structure is quite atom-like, allowing a nearly closed cycle without the need for many repumping lasers. We will also present our work-to-date on laser cooling this molecule. We employ traditional pulsed atomic/molecular beam techniques with a laser vaporization source to generate species with well-defined translational energies over a narrow range of velocity. In this way, we can apply laser-cooling to most species in the beam along a single dimension (the beam’s axis). This project is funded by the LDRD program of the Los Alamos National Laboratory.
The first part of this project involved continued development of theoretical models of diatomic molecular electronic level structure for application to the production of ultracold diatomic molecules via photoassociation. Recently, there has been considerable interest in producing molecules at the temperatures achieved for laser-cooled atoms, for applications to "coherent chemistry," studies of molecule-atom and molecule-molecule interactions. Bose condensates of molecules and for quantum computing. It is advantageous to produce cold molecules from laser-cooled atoms. but this requires an accurate model of the energy level structure near the dissociation limit for excited atoms, and for other intermediate states. With this in mind. we have modeled experimental photoassociation data from Rb2. spectroscopic data on the lowest excited states of Na2, and hyperfine structure of the lowest triplet state of Cs2. The second part involved continued development of experimental techniques for intense atomic beam collimation using a bichromatic laser field. We solved the equations for evolution of atoms in such a laser field, expressed the results in the form of trajectories on the Bloch sphere for a two-level atoms, and then used these results to design and perform efficient atomic beam reflection experiments. At the same time, we are developing methods to use these highly collimated beams of metastable helium atoms for precision lithography, using sensitized surfaces.