Anisotropic Purcell Effect and Quantum Interference in Fractal Aggregates of Nanoparticles

Abstract

We study theoretically the emergence of an anisotropic Purcell factor in random two-dimensional fractal aggregates of nanoparticles. These nanoparticles can either be metallic nanoparticles made of silver, which exhibit surface plasmon resonances, or high-index dielectric nanoparticles like silicon, which possess optical Mie resonances. To calculate the spontaneous emission rates of a quantum emitter, we utilize the electromagnetic Green’s tensor within the framework of the coupled-dipole method. Our findings reveal that the Purcell factor exhibits spatial variations, with certain regions, referred to as hot spots, displaying high values for dipoles oriented within the plane of the fractal aggregate, while dipoles oriented vertically to the aggregate have values close to unity. This anisotropy in the Purcell factor leads to significant quantum interference effects in the spontaneous emission paths of multi-level quantum emitters. As a consequence of this quantum interference, we demonstrate the occurrence of population trapping in a V-type quantum emitter embedded within a fractal aggregate of nanoparticles which cannot otherwise take place if the emitter is placed in vacuum.