# Symmetry and the Geometric Phase in Ultracold Hydrogen-Exchange Reactions

## TL;DR

This paper investigates how geometric phase effects influence ultracold hydrogen-exchange reactions, revealing that symmetry considerations enable experimental measurement of these effects through isotopic variants and symmetry-resolved states.

## Contribution

It demonstrates the role of symmetry in controlling geometric phase effects in ultracold reactions and proposes methods to measure these effects experimentally.

## Key findings

- Geometric phase affects certain final states in ultracold reactions.
- Symmetry considerations allow for experimental detection of GP effects.
- Ultracold reactions reveal fundamental aspects of chemical reactivity.

## Abstract

Quantum reactive scattering calculations are reported for the ultracold hydrogen-exchange reaction and its non-reactive atom-exchange isotopic counterparts, proceeding from excited rotational states. It is shown that while the geometric phase (GP) does not necessarily control the reaction to all final states one can always find final states where it does. For the isotopic counterpart reactions these states can be used to make a measurement of the GP effect by separately measuring the even and odd symmetry contributions, which experimentally requires nuclear-spin final-state resolution. This follows from symmetry considerations that make the even and odd identical-particle exchange symmetry wavefunctions which include the GP locally equivalent to the opposite symmetry wavefunctions which do not. This equivalence reflects the important role discrete symmetries play in ultracold chemistry generally and highlights the key role ultracold reactions can play in understanding fundamental aspects of chemical reactivity.