We report a proof-of-principle experiment for a new method of temperature measurements in waveguide quantum electrodynamics (wQED) experiments, allowing one to differentiate betweenglobal and local baths. The method takes advantage of collective states of two transmon qubits located in the center of a waveguide. The Hilbert space of such a system forms two separate subspaces (bright and dark) which are coupled differently to external noise sources. Measuring transmission through the waveguide allows one to extract separately the temperatures of the baths responsible for global and local excitations in the system. Such a system would allow for building a new type of primary temperature sensor capable of distinguishing between local and global baths.
Multiple atoms coherently interacting with an electromagnetic mode give rise to collective effects such as correlated decay and coherent exchange interaction, depending on the separationof the atoms. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interaction characteristics. We show that there are significant differences in the emerging effects for an array of interacting anharmonic oscillators compared to those of two-level systems and harmonic oscillators. The bosonic decay rate of the most superradiant state increases linearly as a function of the filling factor and exceeds that of two-level systems in magnitude. Furthermore, with bosonic systems, dark states are formed at each filling factor. These are in strong contrast with two-level systems, where the maximal superradiance is observed at half filling and with larger filling factors superradiance diminishes and no dark states are formed. As an experimentally relevant setup of bosonic waveguide QED, we focus on arrays of transmon devices embedded inside a rectangular waveguide. Specifically, we study the setup of two transmon pairs realized experimentally in M. Zanner et al., arXiv.2106.05623 (2021), and show that it is necessary to consider transmons as bosonic multilevel emitters to accurately recover correct collective effects for the higher excitation manifolds.