Spin emitters beyond the point dipole approximation in nanomagnonic cavities

Control over transition rates between spin states of emitters is crucial in a wide variety of fields ranging from quantum information science to the nanochemistry of free radicals. We present an approach to drive a both electric and magnetic dipole-forbidden transition of a spin emitter by placing it in a nanomagnonic cavity, requiring a description of both the spin emitter beyond the point dipole approximation and the vacuum magnetic fields of the nanomagnonic cavity with a large spatial gradient over the volume of the spin emitter. We specifically study the SiV$^-$ defect in diamond, whose Zeeman-split ground states comprise a logical qubit for solid-state quantum information processing, coupled to a magnetic nanoparticle serving as a model nanomagnonic cavity capable of concentrating microwave magnetic fields into deeply subwavelength volumes. Through first principles modeling of the SiV$^-$ spin orbitals, we calculate the spin transition densities of magnetic dipole-allowed and -forbidden transitions and calculate their coupling rates to various multipolar modes of the nanomagnonic cavity. We envision using such a framework for quantum state transduction and state preparation of spin qubits at GHz frequency scales.