Geometric Phase and Interference Effects in Ultracold Chemical Reactions

Abstract

Electronically non-adiabatic effects play an important role in many chemical reactions and light induced processes. Non-adiabatic effects are important, when there is an electronic degeneracy for certain nuclear geometries leading to a conical intersection between two adiabatic Born-Oppenheimer electronic states. The geometric phase effect arises from the sign change of the adiabatic electronic wave function as it encircles the conical intersection between two electronic states (e.g., a ground state and an excited electronic state). This sign change requires a corresponding sign change on the nuclear motion wave function to keep the overall wave function single-valued. Its effect on bimolecular chemical reaction dynamics remains a topic of active experimental and theoretical interrogations. However, most prior studies have focused on high collision energies where many angular momentum partial waves contribute and the effect vanishes under partial wave summation. Here, we examine the geometric phase effect in cold and ultracold collisions where a single partial wave, usually the s-wave, dominates. It is shown that unique properties of ultracold collisions, including isotropic scattering and an effective quantization of the scattering phase shift, lead to large geometric phase effects in state-to-state reaction rate coefficients. Illustrative results are presented for the hydrogen exchange reaction in the fundamental H+H$_2$ system and its isotopic counterparts.