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

具有外部电磁场的超冷原子、分子和离子的量子控制是各种研究领域的核心。一种广泛使用的控制工具利用了原子间长寿命准稳定（共振）态的灵敏度。特别是，磁场可以用来控制原子之间所谓的费什巴赫共振（MFRs），这种特性对于新型量子材料的强相关多体态物质的实验实现至关重要。控制超冷分子相互作用的前景更令人兴奋，因为这些相互作用被预测会产生高度奇异的物质状态，导致高温超导和新的拓扑相。然而，控制分子与外部磁场相互作用的工具远不如控制原子相互作用的工具发达，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性原理计算来探索原子分子碰撞中的MFRs，从而扩大这些可能性。这项研究将为分子间相互作用的精确量子控制铺平道路，并应用于凝聚态系统的量子模拟，以及对被困分子气体的深度同情冷却。目前，数值精确耦合通道（CC）方法还不能用于研究超冷原子-分子碰撞中的磁性费什巴赫共振。这是由于巨大的CC基集造成的极端计算困难，这些基集必须包括所有由强各向异性分子间相互作用耦合的低能振动、旋转和超精细分子态。尤其难以描述的是由于分子中电子和核自旋之间的耦合而产生的众多超精细态，它们在超冷碰撞中起着重要作用。PI建议通过使用灵活的CC基集来解决这个问题，该基集具有不同分子旋转状态的可变数量的超精细基函数。柔性基态的使用可以将CC计算的计算复杂性降低几个数量级，使得计算当前实验感兴趣的超冷原子-分子混合物（如Rb-SrF）中的磁性费什巴赫共振谱在计算上可行。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.