Space-Time Hopfion Crystals

Hopfions, higher-dimensional topological quasiparticles with sophisticated 3D knotted spin textures discovered in condensed matter and photonic systems, show promise in high-density data storage and transfer. Here we present crystalline structures of hopfions lying in space-time constructed by spatiotemporally structured light. A practical methodology using bichromatic structured light beams or dipole arrays to assemble 1D and higher dimensional hopfion lattices is proposed and a technique for tailoring topological orders is elucidated. The birth of photonic hopfion crystals heralds a new era in high-dimensional, condensed, and robust topological information processing.