Geometry of chiral temporal structures I: Physical effects

In non-relativistic 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 in vector space. We apply it to vectors describing 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, non-equilibrium, chiral electron dynamics. We demonstrate that the Berry curvature and Berry connection (i) rely on the polarization properties of light pulses, (ii) can be introduced for multiphoton processes, and (iii) control enantio-sensitive geometric observables via non-equilibrium electronic dynamics excited by tailored laser fields. Our findings may open a way to ultrafast, topologically non-trivial, and enantio-sensitive chemical dynamics.