Multiphoton pulses interacting with multiple emitters in a one-dimensional waveguide

TL;DR

This paper develops a comprehensive theoretical framework for analyzing multiphoton pulses interacting with multiple emitters in a waveguide, accounting for emitter modulation and non-guided modes, enabling detailed predictions of system dynamics and optical properties.

Contribution

It introduces a generalized master equation and input-output relations for complex waveguide-QED systems with multiple emitters and various photon states, advancing the modeling capabilities.

Findings

Derived a generalized master equation for multiphoton interactions.

Calculated real-time dynamics of emitter arrays driven by various photon states.

Developed input-output relations for reflectivity, transmissivity, and pulse shaping.

Abstract

We derive a generalized master equation for multiphoton pulses interacting with multiple emitters in a waveguide-quantum electrodynamics system where the emitter frequency can be modulated and the effects of non-guided modes can also be considered. Based on this theory, we can calculate the real-time dynamics of an array of interacting emitters driven by an incident photon pulse which can be vacuum, a coherent state, a Fock state or their superpositions. Moreover, we also derive generalized input-output relations to calculate the reflectivity and transmissivity of this system. We can also calculate the output photon pulse shapes. Our theory can find important applications in the study of waveguide-based quantum systems.