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

We prove an adiabatic theorem for the ground state of the Dicke model [Phys. Rev. 93, 99 (1954)] 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 affects the rate of approach to the adiabatic limit through a logarithmic correction originating from an infrared singularity characteristic of QED.