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1. Ultracold molecular collisions in magnetic fields: Efficient incorporation of hyperfine structure in the total rotational angular momentum representation

   Timur V. Tscherbul, Jose P. (January 2023, arXivorg)

   The effects of hyperfine structure on ultracold molecular collisions in external fields are largely unexplored due to major computational challenges associated with rapidly proliferating hyperfine and rotational channels coupled by highly anisotropic intermolecular interactions. We explore a new basis set for incorporating the effects of hyperfine structure and external magnetic fields in quantum scattering calculations on ultracold molecular collisions. The basis is composed of direct products of the eigenfunctions of the total {\it rotational} angular momentum (TRAM) of the collision complex Jr and the electron/nuclear spin basis functions of the collision partners. The separation of the rotational and spin degrees of freedom ensures rigorous conservation of Jr even in the presence of external magnetic fields and isotropic hyperfine interactions. The resulting block-diagonal structure of the scattering Hamiltonian enables coupled-channel calculations on highly anisotropic atom-molecule and molecule-molecule collisions to be performed independently for each value of Jr, with an added advantage of eliminating the unphysical states present in the total angular momentum representation. We illustrate the efficiency of the TRAM basis by calculating state-to-state cross sections for ultracold He + YbF collisions in a magnetic field. The size of the TRAM basis required to reach numerical convergence is 8 times smaller than that of the uncoupled basis used previously, providing a computational gain of three orders of magnitude. The TRAM basis is therefore well suited for rigorous quantum scattering calculations on ultracold molecular collisions in the presence of hyperfine interactions and external magnetic fields. 

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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-State-Controlled Collisions of Ultracold Polyatomic Molecules

   https://doi.org/10.1103/w1jn-h3sv  

   Vilas, Nathaniel B; Robichaud, Paige; Hallas, Christian; Tao, Junheng; Anderegg, Loïc; Li, Grace K; Lampson, Hana; Augustovičová, Lucie D; Bohn, John L; Doyle, John M (April 2026, Physical Review X)

   Collisions between ultracold calcium monohydroxide (CaOH) molecules are realized and studied. Inelastic collision rate constants are measured for CaOH prepared in ground and excited vibrational states, and the electric field dependence of these rates is measured for molecules in single quantum states of the parity-doubled bending mode. Theoretical calculations of collision rate coefficients are performed and found to agree with measured values. The lowest collisional loss rates are for states with repulsive long-range potentials that shield ultracold molecules from loss channels at short distance. These results unveil the collisional behavior of parity-doublet molecules in the ultracold regime and lay the foundation for future experiments to evaporatively cool polyatomic molecules to quantum degeneracy. 

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4. SU(N) magnetism with ultracold molecules

   https://doi.org/10.1088/1367-2630/ad89f2  

   Mukherjee, Bijit; Hutson, Jeremy M; Hazzard, Kaden_R A (January 2025, New Journal of Physics)

   Abstract Quantum systems with SU(N) symmetry are paradigmatic settings for quantum many-body physics. They have been studied for the insights they provide into complex materials and their ability to stabilize exotic ground states. Ultracold alkaline-earth atoms were predicted to exhibit SU(N) symmetry for $N=2I+1=1,2,\dots ,10$ , whereIis the nuclear spin. Subsequent experiments have revealed rich many-body physics. However, alkaline-earth atoms realize this symmetry only for fermions with repulsive interactions. In this paper, we predict that ultracold molecules shielded from destructive collisions with static electric fields or microwaves exhibit SU(N) symmetry, which holds because deviations of the s-wave scattering length from the spin-free values are only about 3% for CaF with static-field shielding and are estimated to be even smaller for bialkali molecules. They open the door toNas large as 32 for bosons and 36 for fermions. They offer important features unachievable with atoms, including bosonic systems and attractive interactions. 

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5. Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences

   https://doi.org/10.22331/q-2024-03-28-1304  

   Takou, Evangelia; Barnes, Edwin; Economou, Sophia E (March 2024, Quantum)

   Multipartite entangled states are an essential resource for sensing, quantum error correction, and cryptography. Color centers in solids are one of the leading platforms for quantum networking due to the availability of a nuclear spin memory that can be entangled with the optically active electronic spin through dynamical decoupling sequences. Creating electron-nuclear entangled states in these systems is a difficult task as the always-on hyperfine interactions prohibit complete isolation of the target dynamics from the unwanted spin bath. While this emergent cross-talk can be alleviated by prolonging the entanglement generation, the gate durations quickly exceed coherence times. Here we show how to prepare high-quality GHZ ${}_M$ -like states with minimal cross-talk. We introduce the $M$ -tangling power of an evolution operator, which allows us to verify genuine all-way correlations. Using experimentally measured hyperfine parameters of an NV center spin in diamond coupled to carbon-13 lattice spins, we show how to use sequential or single-shot entangling operations to prepare GHZ ${}_M$ -like states of up to $M=10$ qubits within time constraints that saturate bounds on $M$ -way correlations. We study the entanglement of mixed electron-nuclear states and develop a non-unitary $M$ -tangling power which additionally captures correlations arising from all unwanted nuclear spins. We further derive a non-unitary $M$ -tangling power which incorporates the impact of electronic dephasing errors on the $M$ -way correlations. Finally, we inspect the performance of our protocols in the presence of experimentally reported pulse errors, finding that XY decoupling sequences can lead to high-fidelity GHZ state preparation. 

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