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Multiple emitters coherently interacting with an electromagnetic mode giverise to collective effects such as correlated decay and coherent exchangeinteraction, depending on the separation of the emitters. By diagonalizing theeffective non-Hermitian many-body Hamiltonian we reveal the complex-valuedeigenvalue spectrum encoding the decay and interaction characteristics. We showthat there are significant differences in the emerging effects for an array ofinteracting anharmonic oscillators compared to those of two-level systems andharmonic oscillators. The bosonic decay rate of the most superradiant stateincreases linearly as a function of the filling factor and exceeds that oftwo-level systems in magnitude. Furthermore, with bosonic systems, dark statesare formed at each filling factor. These are in strong contrast with two-levelsystems, where the maximal superradiance is observed at half filling and withlarger filling factors superradiance diminishes and no dark states are formed.As an experimentally relevant setup of bosonic waveguide QED, we focus onarrays of transmon devices embedded inside a rectangular waveguide.Specifically, we study the setup of two transmon pairs realized experimentallyin M. Zanner et al., arXiv.2106.05623 (2021), and show that it is necessary toconsider transmons as bosonic multilevel emitters to accurately recover correctcollective effects for the higher excitation manifolds.

Collective bosonic effects in an array of transmon devices