Photon Scattering from a System of Multi-Level Quantum Emitters. I. Formalism

TL;DR

This paper introduces a comprehensive formalism for analyzing photon scattering from multi-level quantum emitters, enabling direct calculation of scattering dynamics and field amplitudes in weak excitation regimes, applicable to complex geometries.

Contribution

The paper develops a general formalism for photon scattering from multi-level, multi-emitter systems with arbitrary geometry, extending previous methods and enabling direct solutions of scattering dynamics.

Findings

Formalism provides explicit scattered field amplitudes in weak excitation limit.

Applicable to arbitrary geometries and complex emitter configurations.

Lays groundwork for specialized cases in subsequent work (Part II).

Abstract

We introduce a formalism to solve the problem of photon scattering from a system of multi-level 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 multi-emitter and multi-level emitter systems, and is applicable to a plethora of photon scattering problems including conditional state preparation by photo-detection. In this paper, we develop the general formalism for an arbitrary geometry. In the following paper (part II), we reduce the general photon scattering formalism to a form that is applicable to $1$-dimensional waveguides, and show its applicability by considering explicit examples with various emitter configurations.