  I revisit a longstanding question in quantum optics; When is the rotating
wave approximation justified? In terms of the Jaynes-Cummings and Rabi models I
demonstrate that the approximation in general breaks down in the adiabatic
limit regardless of system parameters. This is explicitly shown by comparing
Berry phases of the two models, where it is found that this geometrical phase
is strictly zero in the Rabi model contrary to the non-trivial Berry phase of
the Jaynes-Cummings model. The source of this surprising result is traced back
to different topologies in the two models.
