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We prove an adiabatic theorem for the ground state of the Dicke model in aslowly rotating magnetic field and show that for weak electron-photon coupling,the adiabatic time scale is close to the time scale of the corresponding twolevel system--without the quantized radiation field. There is a correction tothis time scale which is the Lamb shift of the model. The photon field affectthe rate of approach to the adiabatic limit through a logarithmic correctionoriginating from an infrared singularity characteristic of QED.Comment: Revised version, 15 page

Adiabatic theorem without a gap condition: Two-level system coupled to quantized radiation field