  We report on ultrastrong coupling between a superconducting flux qubit and a
resonant mode of a system comprised of two superconducting coplanar stripline
resonators coupled galvanically to the qubit. With a coupling strength as high
as 17% of the mode frequency, exceeding that of previous circuit quantum
electrodynamics experiments, we observe a pronounced Bloch-Siegert shift. The
spectroscopic response of our multimode system reveals a clear breakdown of the
Jaynes-Cummings model. In contrast to earlier experiments, the high coupling
strength is achieved without making use of an additional inductance provided by
a Josephson junction.
