Superluminal correlations in ensembles of optical phase singularities.

Abstract

Phase singularities-points carrying quantized topological charge-are universal features found across diverse wave systems from superfluids and superconductors to acoustic and optical fields^1-4. Ensembles of these singularities exhibit distance correlations resembling particles in liquids^5-8, extensively studied for their role in exotic material phases^9-11. By contrast, the full correlations in phase space that govern the system evolution have remained unexplored and experimentally inaccessible. Here we directly measure the ultrafast dynamics of optical singularity ensembles, capturing their full phase-space correlations, presenting the joint distance-velocity distribution. Our observations show a breakdown of the particle-singularity analogy¹²: phase singularities accelerate towards formally divergent velocities in the moment before annihilation^7,13,14, indicated by measurements of velocities exceeding the speed of light. These apparent superluminal velocities are paradoxically amplified by the slow group velocity of hyperbolic phonon polaritons in our material platform, hexagonal boron nitride membranes^15-19. We demonstrate these phenomena using combined hardware and algorithmic advances in ultrafast electron microscopy^18,20-25, achieving spatial and temporal resolutions, each an order of magnitude below the polaritonic wavelength and cycle period. Our findings deepen our understanding of phase singularities and their universality, enabling to probe topological defect dynamics at previously unattainable timescales.