External Field Control of Ultracold Atom-Molecule Mixtures: Magnetic Feshbach Resonances and Sympathetic Cooling of Polyatomic Molecules

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Quantum control of ultracold atoms, molecules, and ions with external electromagnetic fields is central to a wide variety of research fields. One widely-used control tool utilizes the sensitivity of long-lived quasi-stable (resonant) states between atoms. In particular, magnetic fields can be used to control so-called Feshbach resonances (MFRs) between atoms, a property that has been instrumental to the experimental realization of strongly correlated many-body states of matter for novel quantum materials. The prospect of controlling interactions of ultracold molecules is even more exciting, since these interactions are predicted to give rise to the highly exotic states of matter responsible for high-temperature superconductivity and novel topological phases. However, the tools for controlling molecular interactions with external magnetic fields are much less developed than those for atomic interactions, severely limiting the possibilities for controlling molecular many-body phenomena. The PI proposes to expand these possibilities by exploring MFRs in atom-molecule collisions using rigorous first-principle calculations. The study will pave the way toward precise quantum control of intermolecular interactions with applications to quantum simulation of condensed-matter systems, and to deep sympathetic cooling of trapped molecular gases.At present, numerically exact coupled-channel (CC) methodology cannot be used to study magnetic Feshbach resonances in ultracold atom-molecule collisions. This is due to the extreme computational difficulties caused by enormous CC basis sets, which must include all low-energy vibrational, rotational, and hyperfine molecular states coupled by strongly anisotropic intermolecular interactions. Particularly challenging to describe are the numerous hyperfine states, which arise due to the coupling between the electron and nuclear spins in the molecule, and play an important role in ultracold collisions. The PI proposes to address this issue by using flexible CC basis sets, which feature a variable number of hyperfine basis functions for different molecular rotational states. The use of the flexible basis states could reduce the computational complexity of CC calculations by several orders of magnitude, making it computationally feasible to calculate the spectrum of magnetic Feshbach resonances in ultracold atom-molecule mixtures of current experimental interest (such as Rb-SrF).This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.