Geometry of chiral temporal structures. I. Physical effects

In nonrelativistic physics, the concepts of geometry and topology are usually applied to characterize spatial structures or structures in momentum space. We introduce the concept of temporal geometry, which encompasses the geometric and topological properties of temporal shapes, i.e., trajectories traced by the tip of a time-dependent vector. We apply it to electric field polarizations controlling ultrafast electron currents or induced polarization in chiral molecules. The central concepts of temporal geometry—Berry curvature and Berry connection—emerge as ubiquitous features of photoexcited, nonequilibrium, chiral dynamics. We demonstrate that the Berry curvature and Berry connection (1) rely on the polarization properties of light pulses, (2) can be introduced for multiphoton processes, and (3) control enantiosensitive geometric observables via nonequilibrium electronic dynamics excited by tailored laser fields. Our findings may open a way to ultrafast, topologically nontrivial, and enantiosensitive chemical dynamics.