Adequacy of the Dicke model in cavity QED: A counter-no-go statement

Abstract

The long-standing debate whether the phase transition in the Dicke model can be realized with dipoles in electromagnetic fields is still an unsettled one. The well-known statement often referred to as the ``no-go theorem'' asserts that the so-called ${A}^{2}$ term, missing from the Dicke model, is relevant and prevents the system from undergoing a phase transition. At variance with this common belief, in this paper we prove that the Dicke model does give a proper description of the interaction of light field with the internal excitation of atoms. The phase transition and the spontaneous formation of a transverse-electric mean field cannot be excluded by principle. We point out that the proper treatment of the single-mode approximation is crucial, wherefore we present a systematic derivation of the dipole gauge inside a perfect Fabry-P\'erot cavity from first principles. Besides the impact on the debate around the Dicke phase transition, such a cleanup of the theoretical ground of cavity QED is important because currently there are many emerging experimental approaches to reach strong or even ultrastrong coupling between dipoles and photons, which demand a correct treatment of the Dicke model parameters.