We report on the investigation of a superconducting anharmonic multi-level
circuit that is coupled to a harmonic readout resonator. We observe
multi-photon transitions via virtual energy levels of our system up to the
fifth excited state. The back-action of these higher-order excitations on our
readout device is analyzed quantitatively and demonstrated to be in accordance
with theoretical expectation. By applying a strong microwave drive we achieve
multi-photon dressing within our anharmonic circuit which is dynamically
coupled by a weak probe tone. The emerging higher-order Rabi sidebands and
associated Autler-Townes splittings involving up to five levels of the
investigated anharmonic circuit are observed. Experimental results are in good
agreement with master equation simulations.Comment: 9 pages, 5 figure
