Photon scattering from a system of multilevel quantum emitters. I. Formalism

Abstract

We introduce a formalism to solve the problem of photon scattering from a system of multilevel quantum emitters. Our approach provides a direct solution of the scattering dynamics. As such the formalism gives the scattered fields' amplitudes in the limit of a weak incident intensity. Our formalism is equipped to treat both multiemitter and multilevel emitter systems, and is applicable to a plethora of photon-scattering problems, including conditional state preparation by photodetection. In this paper, we develop the general formalism for an arbitrary geometry. In the following paper (part II) S. Das et al. [Phys. Rev. A 97, 043838 (2018)], we reduce the general photon-scattering formalism to a form that is applicable to one-dimensional waveguides and show its applicability by considering explicit examples with various emitter configurations.