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1. Relativistic aspects of orbital and magnetic anisotropies in the chemical bonding and structure of lanthanide molecules

   https://doi.org/10.1088/1367-2630/ac1a9a  

   Tiesinga, Eite ; Kłos, Jacek ; Li, Ming ; Petrov, Alexander ; Kotochigova, Svetlana ( August 2021 , New Journal of Physics)

   Abstract The electronic structure of magnetic lanthanide atoms is fascinating from a fundamental perspective. They have electrons in a submerged open 4f shell lying beneath a filled 6s shell with strong relativistic correlations leading to a large magnetic moment and large electronic orbital angular momentum. This large angular momentum leads to strong anisotropies, i. e. orientation dependencies, in their mutual interactions. The long-ranged molecular anisotropies are crucial for proposals to use ultracold lanthanide atoms in spin-based quantum computers, the realization of exotic states in correlated matter, and the simulation of orbitronics found in magnetic technologies. Short-ranged interactions and bond formation among these atomic species have thus far not been well characterized. Efficient relativistic computations are required. Here, for the first time we theoretically determine the electronic and ro-vibrational states of heavy homonuclear lanthanide Er 2 and Tm 2 molecules by applying state-of-the-art relativistic methods. In spite of the complexity of their internal structure, we were able to obtain reliable spin–orbit and correlation-induced splittings between the 91 Er 2 and 36 Tm 2 electronic potentials dissociating to two ground-state atoms. A tensor analysis allows us to expand the potentials between the atoms in terms of a sum of seven spin–spin tensor operators simplifying future research. The strengths of the tensor operators as functions of atom separation are presented and relationships among the strengths, derived from the dispersive long-range interactions, are explained. Finally, low-lying spectroscopically relevant ro-vibrational energy levels are computed with coupled-channels calculations and analyzed. 

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2. The Li + CaF → Ca + LiF chemical reaction under cold conditions

   https://doi.org/10.1039/d3cp01464a  

   da Silva, Humberto ; Yao, Qian ; Morita, Masato ; Kendrick, Brian K. ; Guo, Hua ; Balakrishnan, Naduvalath ( May 2023 , Physical Chemistry Chemical Physics)

   The calcium monofluoride (CaF) molecule has emerged as a promising candidate for precision measurements, quantum simulation, and ultracold chemistry experiments. Inelastic and reactive collisions of laser cooled CaF molecules in optical tweezers have recently been reported and collisions of cold Li atoms with CaF are of current experimental interest. In this paper, we report ab initio electronic structure and full-dimensional quantum dynamical calculations of the Li + CaF → LiF + Ca chemical reaction. The electronic structure calculations are performed using the internally contracted multi-reference configuration-interaction method with Davidson correction (MRCI + Q). An analytic fit of the interaction energies is obtained using a many-body expansion method. A coupled-channel quantum reactive scattering approach implemented in hyperspherical coordinates is adopted for the scattering calculations under cold conditions. Results show that the Li + CaF reaction populates several low-lying vibrational levels and many rotational levels of the product LiF molecule and that the reaction is inefficient in the 1–100 mK regime allowing sympathetic cooling of CaF by collisions with cold Li atoms. 

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3. Quantum Metrology with a Molecular Lattice Clock and State-Selected Photodissociation of Ultracold Molecules

   Lee, C.-H. ( January 2020 , Columbia University thesis)

   Over the past few decades, rapid development of laser cooling techniques and narrow-linewidth lasers have allowed atom-based quantum clocks to achieve unprecedented precision. Techniques originally developed for atomic clocks can be extended to ultracold molecules, with applications ranging from quantum-state-controlled ultracold chemistry to searches for new physics. Because of the richness of molecular structure, quantum metrology based on molecules provides possibilities for testing physics that is beyond the scope of traditional atomic clocks. This thesis presents the work performed to establish a state-of-the-art quantum clock based on ultracold molecules. The molecular clock is based on a frequency difference between two vibrational levels in the electronic ground state of 88Sr2 diatomic molecules. Such a clock allows us test molecular QED, improve constraints on nanometer-scale gravity, and potentially provide a model-independent test of temporal variations of the proton-electron mass ratio. Trap-insensitive spectroscopy is crucial for extending coherent molecule-light interactions and achieving a high quality factor Q. We have demonstrated a magic wavelength technique for molecules by manipulating the optical lattice frequency near narrow polarizability resonances. This general technique allows us to increase the coherence time to tens of ms, an improvement of a factor of several thousand, and to narrow the linewidth of a 25 THz vibrational transition initially to 30 Hz. This width corresponds to the quality factor Q = 8 × 10^11. Besides the molecular quantum metrology, investigations of novel phenomena in state-selected photodissociation are also described in this thesis, including magnetic-field control of photodissociation and observation of the crossover from ultracold to quasiclassical chemistry. 

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4. Direct laser cooling of a symmetric top molecule

   https://doi.org/10.1126/science.abc5357  

   Mitra, Debayan ; Vilas, Nathaniel B. ; Hallas, Christian ; Anderegg, Loïc ; Augenbraun, Benjamin L. ; Baum, Louis ; Miller, Calder ; Raval, Shivam ; Doyle, John M. ( September 2020 , Science)

   Ultracold polyatomic molecules have potentially wide-ranging applications in quantum simulation and computation, particle physics, and quantum chemistry. For atoms and small molecules, direct laser cooling has proven to be a powerful tool for quantum science in the ultracold regime. However, the feasibility of laser-cooling larger, nonlinear polyatomic molecules has remained unknown because of their complex structure. We laser-cooled the symmetric top molecule calcium monomethoxide (CaOCH₃), reducing the temperature of ~10⁴molecules from 22 ± 1 millikelvin to 1.8 ± 0.7 millikelvin in one dimension and state-selectively cooling two nuclear spin isomers. These results demonstrate that the use of proper ro-vibronic transitions enables laser cooling of nonlinear molecules, thereby opening a path to efficient cooling of chiral molecules and, eventually, optical tweezer arrays of complex polyatomic species.

    

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5. Raman sideband cooling of molecules in an optical tweezer array

   https://doi.org/10.1038/s41567-023-02346-3  

   Lu, Yukai ; Li, Samuel J. ; Holland, Connor M. ; Cheuk, Lawrence W. ( March 2024 , Nature Physics)

   Ultracold molecules have been proposed as a candidate platform for quantum science and precision measurement because of their rich internal structures and interactions. Direct laser-cooling promises to be a rapid and efficient way to bring molecules to ultracold temperatures. However, for trapped molecules, laser-cooling to the quantum motional ground state remains an outstanding challenge. A technique capable of reaching the motional ground state is Raman sideband cooling, first demonstrated in trapped ions and atoms. Here we demonstrate Raman sideband cooling of CaF molecules trapped in an optical tweezer array. Our protocol does not rely on high magnetic fields and preserves the purity of molecular internal states. We measure a high ground-state fraction and achieve low motional entropy per particle. The low temperatures we obtain could enable longer coherence times and higher-fidelity molecular qubit gates, desirable for quantum information processing and quantum simulation. With further improvements, Raman sideband cooling will also provide a route to quantum degeneracy of large molecular samples, which could be extendable to polyatomic molecular species. 

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