Waveguide QED in the Dipole Gauge

TL;DR

This paper investigates gauge choices in waveguide QED with ultrastrong coupling, demonstrating that the dipole gauge provides accurate results with truncations, revealing novel spectral effects observable via single photon scattering.

Contribution

It extends gauge analysis to waveguide QED, showing the dipole gauge's effectiveness with truncations and identifying new spectral phenomena in scattering spectra.

Findings

Modified primary resonance due to Lamb shift

Asymmetric transmission amplitudes around resonance

Emergence of Fano resonances and inelastic channels

Abstract

In recent studies on ultrastrong coupling between matter and light in cavities, the significance of gauge choice when employing the widely-used two-level approximation has been highlighted. Expanding upon these investigations, we extend the analysis to waveguide QED, where we demonstrate that truncations performed in the dipole gauge also yield accurate results. To illustrate this point, we consider the case of a dipole coupled to a cavity array. Various numerical and analytical techniques have been employed to investigate the low-energy dynamics of the system. Leveraging these theoretical tools, we argue that single photon scattering is an ideal method for investigating gauge-related issues. Our findings reveal two novel effects in the scattering spectra, which cannot be reproduced in a truncated model using the Coulomb gauge. Firstly, the primary resonance is modified due to a Lamb shift contribution. Secondly, we observe asymmetric transmission amplitudes surrounding this resonance, reflecting the asymmetry of the spectral density in this model. Additionally, we explore other features in the scattering spectra resulting from ultrastrong couplings, such as the emergence of Fano resonances and inelastic channels. Finally, we propose an experimental test of our ideas in the context of circuit QED.