Geometry of chiral temporal structures II: The formalism

TL;DR

This paper develops a differential geometric formalism to understand how chiral molecules exhibit enantio-sensitive responses to light, focusing on the role of Berry connection and curvature in light-driven electronic states.

Contribution

It introduces a novel geometric framework linking molecular enantio-sensitivity to Berry curvature and connection in the context of light-molecule interactions.

Findings

Enantio-sensitive observables are derived from geometric properties of molecular responses.

The formalism connects molecular chirality with geometric phases in light-driven states.

Provides a foundation for predicting enantio-sensitive effects using differential geometry.

Abstract

We develop a mathematical formalism underlying the emergence of enantio-sensitive molecular orientation due to photoionization or photoexitation of chiral molecules. We consider geometric quantities such as the Berry connection and Berry curvature in light-driven chiral electronic states in the space of complex light polarization vectors. The parametric dependence of the light-driven electronic wavefunction on such vectors emerges due to various possible mutual orientations between the laser field and a chiral molecule. Using the tools of differential geometry we show how the enantio-sensitive observables emerge from the geometry of the molecular response in such spaces.