  In this work, we irradiate a superconducting artificial molecule composed of
two coupled tunable transmons with microwave light while monitoring its state
via joint dispersive readout. Performing high-power spectroscopy, we observe
and identify a variety of single- and multiphoton transitions. We also find
that at certain fluxes, the measured spectrum of the system deviates
significantly from the solution of the stationary Schr\"odinger equation with
no driving. We reproduce these unusual spectral features by solving numerically
the full master equation for a steady-state and attribute them to an
Autler-Townes-like effect in which a single tone is simultaneously dressing the
system and probing the transitions between new eigenstates. We show that it is
possible to find analytically the exact frequencies at which the satellite
spectral lines appear by solving self-consistent equations in the rotating
frame. Our approach agrees well with both the experiment and the numerical
simulation.
