Effects of Modal Dispersion on Few Photon - Qubit Scattering in One-Dimensional Waveguides

TL;DR

This paper investigates how modal dispersion affects single- and two-photon scattering in a one-dimensional waveguide with a qubit, developing a theoretical framework and numerical methods to analyze photon trapping and correlations.

Contribution

It introduces a multichannel scattering theory incorporating modal dispersion effects and derives closed-form formulas for photon trapping rates using Feynman diagrams.

Findings

Modal dispersion creates atom-photon bound states.

The formalism accurately predicts photon trapping rates.

Numerical results confirm the theoretical predictions.

Abstract

We study one- and two-photon scattering from a qubit embedded in a one-dimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersion leads to atom-photon bound states which necessitate the use of multichannel scattering theory. We present multichannel scattering matrix elements in terms of the solution of a Fredholm integral equation of the second kind. Through the use of the Lippmann-Schwinger equation, we derive an infinite series of Feynman diagrams that represent the solution to the integral equation. We use the Feynman diagrams as vertex correction terms to come up with closed form formulas that successfully predict the trapping rate of a photon in the atom-photon bound state. We verify our formalism through Krylov-subspace based numerical studies with pulsed excitations. Our results provide the tools to calculate the complex correlations between scattered photons in a dispersive environment.