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

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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.