Coupled quantum vortex kinematics and Berry curvature in real space

Geometrical aspects underlying the cosmos and its laws have been put in emphasis since Einstein. Later on, the Berry curvature provided a powerful unifying tool among several branches of science and topology. Topological defects or quantum vortices have been under the spotlight, as quanta of rotation in condensates, superfluids, and optics. Here, we use microcavity polaritons to imprint a dynamical pseudospin texture, whose reshaping involves both the ultrafast spiraling of the vortex cores and the associated Berry curvature itself. The pseudospin topology is a double conformal mapping of the whole Bloch sphere of states, whose projection density is represented by the curvature. Any evolution of the states on the sphere is imaged to the real space plane mediated by this link. We show that polaritons represent a tailored system to study the Berry concepts and invoke a new role of the curvature in describing the vortex cores' velocity directly in real space.