Photon scattering from a system of multilevel quantum emitters. II. Application to emitters coupled to a one-dimensional waveguide

摘要

In a preceding paper we introduced a formalism to study the scattering of low-intensity fields from a system of multilevel emitters embedded in a three-dimensional (3D) dielectric medium. Here we show how this photonscattering relation can be used to analyze the scattering of single photons and weak coherent states from any generic multilevel quantum emitter coupled to a one-dimensional (1D) waveguide. The reduction of the photon-scattering relation to 1D waveguides provides a direct solution of the scattering problem involving low-intensity fields in the waveguide QED regime. To show how our formalism works, we consider examples of multilevel emitters and evaluate the transmitted and reflected field amplitude. Furthermore, we extend our study to include the dynamical response of the emitters for scattering of a weak coherent photon pulse. As our photon-scattering relation is based on the Heisenberg picture, it is quite useful for problems involving photodetection in the waveguide architecture. We show this by considering a specific problem of state generation by photodetection in a multilevel emitter, where our formalism exhibits its full potential. Since the considered emitters are generic, the 1D results apply to a plethora of physical systems such as atoms, ions, quantum dots, superconducting qubits, and nitrogen-vacancy centers coupled to a 1D waveguide or transmission line.