  We revisit earlier studies on Berry phases suggested to appear in certain
cavity QED settings. It has been especially argued that a non-trivial geometric
phase is achievable even in the situation of no cavity photons. We, however,
show that such results hinge on imposing the {\it rotating wave approximation}
(RWA), while without the RWA no Berry phases occur in these schemes. A
geometrical interpretation of our results is obtained by introducing
semi-classical energy surfaces which in a simple way brings out the phase space
dynamics. With the RWA, a conical intersection between the surfaces emerges and
encircling it gives rise to the Berry phase. Without the RWA, the conical
intersection is absent and therefore the Berry phase vanishes. It is believed
that this is a first example showing how the application of the RWA in the
Jaynes-Cummings model may lead to false conclusions, regardless mutual
strengths between the system parameters.
