Universal Few-body Quantum States and Interactions

The processes being tackled in this project are centered on identifying critical interactions and reactions needed to understand and control the behavior of atoms and molecules, and their interactions with light. The various systems targeted for study require the detailed quantum mechanical description of several simultaneously interacting particles, be they atoms, molecules, or atomic nucleons. This class of quantum mechanical problems constitutes the field of few-body physics, and as the number of particles increases, the difficulty of solving the quantum mechanical equations grows exponentially: Few previous studies have successfully ventured beyond the celebrated 3-body problem. In this project, novel and unconventional techniques are developed and extended, including the adoption of atypical coordinate systems and novel representations of the quantum states, thereby enabling results for 3-body, 4-body and even 5-body problems. The goals of the project include concrete and detailed predictions of the behavior, energy level structure, and reaction rates amenable to experimental verification, including some which would support ongoing efforts to advance quantum information science. The project is expected to yield credible predictions of new phenomena and to stimulate qualitative insights that might suggest new paths for furthering the advance of this field of research. The effort will also strengthen the pool of talent capable of tackling the most challenging theoretical questions in the microscopic world. The specific topics being studied involve few-body systems at nanokelvin temperatures that are of current interest in the realm of ultracold atomic and molecular physics. One area is the development of the quantum theory of three-body recombination in an ultracold gas of microwave-shielded polar molecules, which is a key loss process in that system which remains poorly understood. An adiabatic representation in hyperspherical coordinates will be implemented to describe this process and explore novel bound states known as Efimov states. Another area of concentration for the project is the delicate binding of Rydberg molecules to a ground state atom at enormous length scales, separated by hundreds or even thousands of Bohr radii. A recently developed Green's function method can be applied to quantitatively describe the spectroscopy at high resolution, as well as to predict related collisional phenomena such as associative ionization or predissociation. 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.