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

超冷原子、分子和离子在外加电磁场作用下的量子控制是许多研究领域的核心问题。一种广泛使用的控制工具是利用原子之间长寿命准稳定(共振)状态的敏感性。特别是，磁场可以用来控制原子之间的所谓费什巴赫共振(MFR)，这一特性有助于在实验中实现新型量子材料的强关联多体物质状态。控制超冷分子相互作用的前景更加令人兴奋，因为这些相互作用被预测为导致高温超导的高度奇异的物质状态和新的拓扑相。然而，用于控制分子与外部磁场相互作用的工具远远落后于用于控制原子相互作用的工具，这严重限制了控制分子多体现象的可能性。PI建议通过使用严格的第一原理计算来探索原子-分子碰撞中的MFR来扩展这些可能性。这项研究将为精确的分子间相互作用的量子控制铺平道路，并应用于凝聚态系统的量子模拟，以及囚禁分子气体的深度共振冷却。目前，数值精确耦合通道(CC)方法还不能用于研究超冷原子-分子碰撞中的磁性Feshbach共振。这是由于巨大的CC基组造成了极大的计算困难，它必须包括所有通过强烈各向异性分子间相互作用耦合的低能振动、转动和超精细分子状态。特别具有挑战性的是大量的超精细态，它们是由于分子中电子和核自旋之间的耦合而产生的，在超冷碰撞中发挥着重要作用。PI建议通过使用灵活的CC基组来解决这个问题，该基组具有针对不同分子旋转态的可变数量的超精细基函数。灵活基态的使用可以将CC计算的计算复杂性降低几个数量级，使计算当前有实验意义的超冷原子-分子混合物(如RB-SRF)中的磁性Feshbach共振谱成为可能。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.