  We study dressed Bose-Einstein condensates in an atom chip radio-frequency
trap. We show that in this system sufficiently strong dressing can be achieved
to cause the widely used rotating wave approximation (RWA) to break down. We
present a full calculation of the atom - field coupling which shows that the
non-RWA contributions quantitatively alter the shape of the emerging dressed
adiabatic potentials. The non-RWA contributions furthermore lead to additional
allowed transitions between dressed levels. We use RF spectroscopy of
Bose-Einstein condensates trapped in the dressed state potentials to directly
observe the transition from the RWA to the beyond-RWA regime.
