Global vs local bath in superconducting waveguide QED experiments.

Characterizing and controlling the coupling between qubits and environmental degrees of freedom are one of the central problems for engineering quantum systems towards applications. In some cases, the coupling might be useful as in quantum enhanced detecting schemes, or harmful e.g for quantum computation protocols, leading to an additional dephasing as well as excessive qubit population. The coupling of one quantum system to multiple environmental degrees of freedom attracted significant attention during the last years both on theoretical and experimental sides, especially in the field of superconducting quantum circuits. Most of the recent work addresses this problem from the side of cavity Quantum Electrodynamics (cQED), concentrating on individual and/or collective dephasing introduced by resonators dispersively coupled to the qubit. In this work we investigate the problem in the context of 3D waveguide Quantum Electrodynamics (wQED). We show that in a typical experimental situation the environment can be effectively considered as consisting of a global and a local bath. We realize an experimental protocol where we use collective dark and bright states to extract the respective temperatures of the two baths.