Entangled nanoparticles: discovery by visualization in 4D electron microscopy.

Particle interactions are fundamental to our understanding of nanomaterials and biological assemblies. Here, we report on the visualization of entangled particles, separated by as large as 70 nm, and the discovery of channels in their near-fields. For silver nanoparticles, the induced field of each particle extends to 50-100 nm, but when particles are brought close in separation we observe channels as narrow as 6 nm, a width that is 2 orders of magnitude smaller than the incident field wavelength. The channels' directions can be controlled by the polarization of the incident field, particle size, and separation. For this direct visualization of these nanoscopic near-fields, the high spatial, temporal, and energy resolutions needed were hitherto not possible without the methodology given here. This methodology, we anticipate, paves the way for further fundamental studies of particle entanglement and for possible applications spanning materials and macromolecular assemblies.