  We experimentally studied the microwave response of a transmon artificial
atom coupled to two closely spaced resonant modes. When the atom is under
driven with one of the modes, the atom state and mode photons are superposed,
forming the dressed states. Dressed states with 1st, 2nd and 3rd excited states
of the atom were prepared and probed via the strong coupling to the other
resonant mode from the point of view of cavity quantum electrodynamics. The
transmission of the probe tone is modulated by the driving microwave amplitude,
displaying multi-photon process associated with the inter-atomic level
transitions. Our system provides an easy method to study the dressed states by
driving one mode and probing the Landau-Zener transition of the other.
