Many-body states of radiation and quantum thermalization in multi-mode circuit QED (Part 1)

We explore a quantum impurity problem arising from the galvanic coupling of a superconducting fluxonium qubit to a long section of a 1D waveguide. The resulting multi-mode circuit QED has presented theoretical challenges in the context of gauge invariance and convergence of perturbative expansions. The fluxonium’s strong anharmonicity prevents the use of semi-classical black-box circuit quantization procedure, standard to transmon-based circuits. We have uncovered a qualitatively new effect, the dressing of photons by photons: a one-photon state hybridizes with nearly resonant n-photon states. In the spectral range 5-7 GHz, we resolve two-photon and three-photon splittings and reproduce hundreds of energy levels without adjustable parameters via an Hamiltonian with asymptotic freedom and truncation-friendly gauge. We observe a fine structure of discrete many-body resonances that turns into a broad continuum as we go to higher energies. This occurs because the density of multi-photon states rapidly grows with increasing energy. Such transition shows that our finite-size 1D quantum system can act as a bath to itself. We believe this is the first instance of quantum thermalization of radiation in a closed system.