RUI: Collaborative Research: The Role of Microscopic Molecular Structure in Confined Bose-Einstein Condensates of Diatomic Molecules

双原子分子只由两个原子组成，是能存在的最简单的分子。然而，尽管双原子分子的结构相对简单，但通过原子周围电子的重叠结构将两个原子结合在一起的分子，显示出丰富的内部结构，可以影响双原子分子与周围其他分子相互作用的系统的行为。这个合作的理论研究项目旨在了解双原子分子的微观结构如何影响超冷分子气体的整体行为。该计划的目标是了解分子相互作用和内部分子结构的细节如何在分子玻色-爱因斯坦凝聚体中的紧急整体现象中发挥作用，并为正在进行的实验提供指导和动力。此外，这项研究旨在促进在少体和多体量子物理专业的科学家之间的合作，并在整个研究过程中整合本科生研究人员。特别是，学生们参与开发理论工具和实施数值计算，并在科学会议上发表论文，准备提交给同行评议的期刊的手稿。这个项目的重点是玻色子分子的量子简并气体，其中分子的空间和微观自由度影响整体系统的行为。与许多传统的凝聚态或固态系统不同，超冷分子的量子简并气体为我们提供了对其微观和整体性质的极大控制，它们允许在独特的背景下研究集体的、涌现的量子现象。在双原子分子样品中实现量子简并的最新实验进展有望显著提高超冷量子系统的实用性。这项研究的动机是，空间和微观自由度的相互作用可以导致量子多体系统中各种丰富的行为，例如相互作用驱动的两体水平的自旋-轨道耦合，以及表现出强烈依赖于约束几何的依赖于状态的偶极相互作用。使用平均场和微扰量子场理论方法，(1)推广了分子玻色气体的两态模型，以解释现实的实验场景，包括有限的囚禁几何、任意的极化场和短程相互作用；(2)扩展该模型以包括更多的微观态，并将其应用于描述具有大有效自旋自由度的刚性转子分子的玻色气体；以及(3)在模型中加入超偶极相互作用，如四极相互作用和有耗碰撞。这项工作的长期目标是建立对双原子分子微观结构如何影响分子间相互作用的严格理论理解，从而在新兴的量子多体现象中发挥作用，并为不久的将来可用的量子简并分子的实验提供指导和动力。

Diatomic molecules, consisting of only two atoms, are the simplest molecules that can exist. Yet, although the structure of diatomic molecules is comparatively simple, the molecule, with the two atoms bound together through the overlapping structure of the electrons surrounding the atoms, demonstrates a rich internal structure that can influence the behavior of a system in which the diatomic molecule interacts with other molecules surrounding it. This collaborative theoretical research program is aimed at understanding how the microscopic structure of diatomic molecules influences the bulk behavior of ultracold molecular gases. The goals of the program are to understand how the details of the molecular interactions and internal molecular structure play a role in emergent bulk phenomena in molecular Bose-Einstein condensates, and to provide guidance and motivation for ongoing experiments. Additionally, this research is designed to foster collaborations between scientists with specializations in few-body and many-body quantum physics, and integrate undergraduate student researchers in the entirety of the research process. In particular, students are involved in developing theoretical tools and implementing numerical calculations, and are presenting at scientific meetings and preparing manuscripts for submission to peer reviewed journals. The focus of this project is quantum degenerate gases of bosonic molecules in which the spatial and microscopic degrees of freedom of the molecules influence the bulk system behavior. Unlike many conventional condensed matter or solid state systems, quantum degenerate gases of ultracold molecule provide us with a great deal of control over both their microscopic and bulk properties, and they permit the investigation of collective, emergent quantum phenomena in unique contexts. Recent experimental progress towards the realization of quantum degeneracy in samples of diatomic molecules promises to significantly enhance the utility of ultracold quantum systems. This research is motivated by the idea that the interplay of spatial and microscopic degrees of freedom can lead to a variety of rich behaviors in quantum many-body systems, such as an interaction driven spin-orbit coupling at the two-body level and state-dependent dipolar interactions that exhibit strong dependence on confinement geometry. Using mean-field and perturbative quantum field theory methods, this research (1) generalizes a two-state model of a molecular Bose gas to account for realistic experimental scenarios, including finite trapping geometries, arbitrary polarization fields, and short-range interactions; (2) extends the model to incorporate more microscopic states and apply it to describe Bose gases of rigid rotor molecules with large effective spin degrees of freedom; and (3) incorporates beyond-dipolar interactions, such as quadrupolar interactions and lossy collisions, into the model. The long term goals of this work are to develop a rigorous theoretical understanding of how the microscopic structure of diatomic molecules influence intermolecular interactions, and thereby play a role in emergent quantum many-body phenomena, and to provide guidance and motivation for experiments with quantum degenerate molecules that will be available in the near future.