  We prove an adiabatic theorem for the ground state of the Dicke model in a
slowly rotating magnetic field and show that for weak electron-photon coupling,
the adiabatic time scale is close to the time scale of the corresponding two
level system--without the quantized radiation field. There is a correction to
this time scale which is the Lamb shift of the model. The photon field affect
the rate of approach to the adiabatic limit through a logarithmic correction
originating from an infrared singularity characteristic of QED.
