Dynamical excitation control and multimode emission of an atom-photon bound state

Atom-photon bound states arise from the coupling of quantum emitters to the band edge of dispersion-engineered waveguides. Thanks to their tunable-range interactions, they are promising building blocks for quantum simulators. Here, we study the dynamics of an atom-photon bound state emerging from coupling a frequency-tunable quantum emitter - a transmon-type superconducting circuit - to the band edge of a microwave metamaterial. Employing precise temporal control over the frequency detuning of the emitter from the band edge, we examine the transition from adiabatic to non-adiabatic behavior in the formation of the bound state and its melting into the propagating modes of the metamaterial. Moreover, we experimentally observe multi-mode emission from the bound state, triggered by a fast change of the emitter's frequency. Our study offers insight into the dynamic preparation of atom-photon bound states and provides a method to characterize their photonic content, with implications in quantum optics and quantum simulation.