## "Manipulating emission rates and interactions of quantum emitters beyond electric dipole approximation"
Interaction of a quantum emitter with the surrounding photonic bath in its ground state yields a correction to the emitter?s transition energy, referred to as Lamb shift, and gives rise to the process of spontaneous emission. If multiple emitters are present, shared photonic bath acts as a carrier of interactions between them and is responsible for collective emission. An example is the phenomenon of Dicke superradiance. The spatial and spectral structure of photonic bath of a quantum emitter can be tailored, e.g. with traditional cavities or with nanostructured materials. The most extreme illustration of impact of nanostructured surroundings on optical properties of emitters is enhancement by many orders of magnitude of spontaneous emission rates of molecules adjacent to plasmonic nanoparticles. The reason for such a remarkable influence of plasmonic nanoparticles is their capability, upon illumination, of strong electromagnetic field confinement to subwavelength regions of space. There, the density of photonic states, which the quantum emitter can couple to, is locally increased. Subwavelength confinement suggests, however, that the paradigmatic approach to light-matter interaction within the electric dipole approximation may not be sufficient, and steps beyond may be required [1,2]. These steps include influence of higher-order multipoles such as magnetic dipole or electric quadrupole, which scale proportionally to spatial modulations of
electric field. To evaluate the impact of nanoparticles on properties of emitters we use the dyadic Green?s tensor formalism following Refs. [3,4] and generalize it beyond the electric dipole approximation. For this purpose we consider quantum emitters? transitions characterized simultaneously by multiple moments: the electric dipole, magnetic dipole, and electric quadrupole. Remarkably, the optical properties of the photonic bath are described by a classical quantity: the electromagnetic Green's tensor. In particular, it accounts for the geometry and material properties of the nanoparticle which the quantum emitter is adjacent to. In this framework we solve Heisenberg equations for field and emitters? operators dynamics combined with the Markovian approximation, to arrive at the desired expressions for transition rates and interaction strengths. To provide examples, we apply the formalism to simple geometries like a planar interface between two different media or a nanoparticle, and identify scenarios where a step beyond the electric dipole approximation is necessary for accurate description of emitters? dynamics. References: [1] Rivera, N., Kaminer, I., Zhen, B., Joannopoulos, J. D., & Solja?i?, M., Shrinking light to allow forbidden transitions on the atomicscale. Science, 353(6296), 263-269 (2016). [2] Kosik M., Spontaneous emission enhancement beyond dipole approximation: a Green?s functions approach (Master?s thesis), 2017. [3] Dung, H. T., Knöll L., Welsch D.-G., Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics, Phys. Rev. A 57, 3931 (1998). [4] Dzsotjan D., Sřrensen A.S., Fleischhauer M., Quantum emitters coupled to surface plasmons of a nanowire: A Green?sfunction approach, Phys. Rev. B 82, 075427 (2010). Host: Andres Ayuela and Marta Pelc |