Abstract: Broken symmetries are ubiquitous in physics, and they are associated with ferromagnetism, nonreciprocal effects, optical activity, and vortex beams of photons and electrons. In some cases, the symmetry breakdown also leads to the formation of various topological solutions or defects of a continuous field. In the first part of the talk, I will show how we developed state-of-the-art x-ray nanoimaging and femtosecond time-resolved scattering methods to probe topological spin textures. Our new microscopic approach provides a world-record 3D 10nm vector resolution with more than 150nm penetration depth. We then used it to observe emergent topological magnetic monopoles (namely, magnetic hedgehogs or Bloch points) and magnetic skyrmion lattice for the first time [1,2]. In the second part of the talk, we will look into singular optics and topologies of light. Examples include the creation and characterization of time-varying and space-time vortices of light [3, 4], as well as novel scattering and imaging methods enabled by them.
References:  Science Advances 5, eaax3009 (2019);  ArXiv:2104.12933 (2021);  Science 364, eaaw9486 (2019);  Nature Photonics 15, 608 (2021).