Few-mode Field Quantization for Multiple Emitters

The control of the interaction between several quantum emitters using nanophotonic structures holds great promise for quantum technology applications. However, the theoretical description of such processes for complex nanostructures is a highly demanding task as the electromagnetic (EM) modes are in principle described by a high-dimensional continuum. We here introduce an approach that permits a quantized description of the full EM field through a "minimal" number of discrete modes. This extends the previous work in [Medina et al., Phys. Rev. Lett. 126, 093601 (2021)] to the case of an arbitrary number of emitters with arbitrary orientations, without any restrictions on the emitter level structure or dipole operators. We illustrate the power of our approach for a model system formed by three emitters placed in different positions within a metallodielectric photonic structure consisting of a metallic dimer embedded in a dielectric nanosphere. The low computational demand of this method makes it suitable for studying dynamics for a wide range of parameters. We show that excitation transfer between the emitters is highly sensitive to the properties of the hybrid photonic-plasmonic modes, demonstrating the potential of such structures for achieving control over emitter interactions.