  A superconducting qubit was driven in an ultrastrong fashion by an
oscillatory microwave field, which was created by coupling via the nonlinear
Josephson energy. The observed Stark shifts of the `atomic' levels are so
pronounced that corrections even beyond the lowest-order Bloch-Siegert shift
are needed to properly explain the measurements. The quasienergies of the
dressed two-level system were probed by resonant absorption via a cavity, and
the results are in agreement with a calculation based on the Floquet approach.
