Theory and simulations of few-photon Fock state pulses strongly interacting with a single qubit in a waveguide: exact population dynamics and time-dependent spectra

TL;DR

This paper develops an exact quantum theory and simulations for few-photon pulses interacting with a two-level system in a waveguide, revealing detailed population dynamics and spectra beyond weak excitation approximations.

Contribution

It provides analytical solutions for TLS population and spectra for 1- and 2-photon pulses, and employs matrix product state simulations for general pulses, extending understanding of waveguide-QED interactions.

Findings

Exact expressions for TLS population and spectra for 1- and 2-photon pulses.

Population effects are significant even for long pulses, invalidating weak excitation assumptions.

Matrix product state simulations confirm analytical results and explore complex photon correlations.

Abstract

We present a detailed quantum theory and simulations of a few-photon Fock state pulse interacting with a two-level system (TLS) in a waveguide. For a rectangular pulse shape, we present an exact temporal scattering theory for the waveguide-QED system to derive analytical expressions for the TLS population, for 1-photon and 2-photon pulses, for both chiral and symmetric emitters. We also derive the stationary (long time) and time-dependent spectra for 1 photon excitation, and show how these differ at a fundamental level when connecting to TLS population effects. Numerically, we also present matrix product state (MPS) simulations, which allow us to compute more general photon correlation functions for arbitrary quantum pulses, and we use this approach to also show results for Gaussian quantum pulses, and to confirm the accuracy of our analytical results. In addition, we show how significant population TLS effects also occur for pulses relatively long compared to the radiative decay time (showing that a weak excitation approximation cannot be made), and investigate the population signatures, nonlinear features and dynamical behavior as a function of pulse length. These detailed theoretical results extend and complement our related Letter results [Arranz Regidor et al., unpublished, 2024].