Exploring Contacts in a New Era: Spin-Orbit Coupling and Dimension Crossover

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The pursuit of universal laws has been a long-term effort in physics. In classical mechanics, Newton's laws could explain a vast range of phenomena, including the falling of an apple from a tree and the orbiting of planets around the sun. In quantum mechanics, however, it is much more difficult to identify universal physical laws, since it is notably difficult to solve Schrodinger's equation for quantum systems composed of many interacting particles. This is unfortunate as the bulk of all systems consist of many interacting particles. Ultracold atoms provide physicists a promising platform to reveal universal principles in the quantum world. Due to the fact that the average particle-particle spacing is much larger than the range of interactions between charge-neutral atoms, the so-called "contacts" can be used to establish a variety of potentially powerful universal relations, which are valid regardless of microscopic parameters of the ultracold atoms themselves. Such universal relations bring physicists a conceptually novel means to understand and explore quantum many-body physics. This project will explore the use of "contacts" in ultracold gases in the hope of identifying new universal relations in many-body systems. Recent experimental developments offer physicists unprecedented opportunities to study contacts and universal relations. Synthetic spin-orbit couplings have been realized in many experimental groups. These novel couplings fundamentally influence the short-range asymptotic behavior of many-body wavefunctions and are expected to produce unexplored universal relations. External trapping potentials can continuously change the dimension of a quantum system. Traditional results derived for a given dimension no longer apply in such dimensional crossovers. This project aims to use spin-orbit coupling and dimensional crossover as unique tools to explore a new era of contacts. Topics include delivering new universal relations, engineering unconventional effective Hamiltonians for creating novel few- and many-body states, and implementing contacts as a new scheme for tracing quantum many-body phenomena. The outcome of this project will provide new insights into bridging few- and many-body physics using contacts.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.