Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms

TL;DR

This paper develops an input-output theoretical framework for waveguide QED with inhomogeneous atoms, revealing collective effects like superradiance and subradiance, and aligns with recent experimental findings using superconducting qubits.

Contribution

It extends previous models by deriving an effective master equation for inhomogeneous atoms and analyzes scattering to study collective phenomena in waveguide QED.

Findings

Analytical and numerical results show collective effects influence scattering properties.

Theoretical predictions match recent experimental data with superconducting qubits.

Changing atom frequencies simulates varying atom-atom distances and collective behaviors.

Abstract

We study the collective effects that emerge in waveguide quantum electrodynamics where several (artificial) atoms are coupled to a one-dimensional superconducting transmission line. Since single microwave photons can travel without loss for a long distance along the line, real and virtual photons emitted by one atom can be reabsorbed or scattered by a second atom. Depending on the distance between the atoms, this collective effect can lead to super- and subradiance or to a coherent exchange-type interaction between the atoms. Changing the artificial atoms transition frequencies, something which can be easily done with superconducting qubits (two levels artificial atoms), is equivalent to changing the atom-atom separation and thereby opens the possibility to study the characteristics of these collective effects. To study this waveguide quantum electrodynamics system, we extend previous work and present an effective master equation valid for an ensemble of inhomogeneous atoms driven by a coherent state. Using input-output theory, we compute analytically and numerically the elastic and inelastic scattering and show how these quantities reveal information about collective effects. These theoretical results are compatible with recent experimental results using transmon qubits coupled to a superconducting one-dimensional transmission line [A.~F.~van Loo {\it et al.}].