Renormalization Treatment of IR and UV Cutoffs in Waveguide QED and Implications to Numerical Model Simulation

TL;DR

This work addresses how finite infrared and ultraviolet cutoffs in numerical waveguide QED simulations shift observable atomic properties. It develops a non-perturbative, first-principles renormalization framework in the time domain to relate bare model parameters to physically measurable quantities and to connect with standard scattering theory and Green's function formalisms. The authors derive explicit relations for the physical atomic frequency and decay rate as functions of the bare parameters and the cutoff window, including a Lamb-shift–type logarithmic correction, and propose a renormalization-aware end-to-end parameterization that enables accurate, computation-efficient simulations with reduced bandwidth. The approach extends naturally to multi-photon scattering, offering a practical route to reliable light-matter simulators and guiding extensions to more complex configurations.

Abstract

We present a non-perturbative, first-principles derivation of renormalization relations for waveguide-QED models, explicitly accounting for the infrared (IR) and ultraviolet (UV) cutoffs that are necessarily introduced in numerical simulations. By formulating the atomic dynamics in the time domain, we obtain explicit expressions linking the bare model parameters to the physically observable atomic frequency and decay rate, and verify their consistency with scattering theory. We further connect these results to standard Feynman diagrams, providing a transparent physical interpretation and ensuring the generality of the approach. Finally, we show how these renormalization relations can be used to parameterize simulations with a minimal frequency bandwidth, simultaneously preserving physical accuracy and reducing computational cost, thereby paving the way for efficient and reliable multi-photon light-matter simulations.

Figures (7)

• Figure 1: Schematic representation of the waveguide QED setup under consideration. Panel (a) illustrates the case where the two channels correspond to right- and left-moving modes of a single waveguide, while panel (b) depicts the case of two distinct waveguides, each supporting unidirectional propagation.
• Figure 2: Time evolution of the quantities $\mathcal{R}_n$, $\mathcal{T}_n$, and $\mathcal{A}_n$ for the three different values of $\Lambda_{\mathrm{UV}}$. Because the time step is small, the curves appear continuous, although they are obtained from consecutive discrete time steps.
• Figure 3: Reflection probability at resonance $\omega_p = \omega_0$ as a function of the UV cutoff $\Lambda_{\mathrm{UV}}$.
• Figure 4: Comparison between the numerically obtained reflection coefficient $\mathcal{R}$ and the prediction $\mathcal{R}^{\text{(th)}}$ across various frequency windows.
• Figure 5: Comparison between the numerically obtained reflection coefficient $\mathcal{R}$ and the adjusted prediction $\mathcal{R}^{(\text{phys})}$ derived from the physical parameters, evaluated across different frequency windows. The bare prediction $\mathcal{R}^{(0)}$ is shown for reference.