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

TL;DR

This paper challenges the traditional no-go theorem by demonstrating that the Dicke model can indeed describe phase transitions in cavity QED when using the dipole gauge, emphasizing the importance of the single-mode approximation.

Contribution

It provides a systematic derivation of the Dicke model in the dipole gauge from first principles, countering the no-go theorem and clarifying the conditions for phase transitions in cavity QED.

Findings

The Dicke model can exhibit phase transitions in the dipole gauge.

The single-mode approximation is crucial for accurate modeling.

A systematic derivation of the dipole gauge in cavity QED is presented.

Abstract

The long-standing debate whether the phase transition in the Dicke model can be realized with dipoles in electromagnetic fields is yet an unsettled one. The well-known statement often referred to as the "no-go theorem", asserts that the so-called A-square term, just in the vicinity of the critical point, becomes relevant enough to prevent 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 consistent description of the interaction of light field with the internal excitation of atoms, but in the dipole gauge of quantum electrodynamics. The phase transition cannot be excluded by principle and a spontaneous transverse-electric mean field may appear. We point out that the single-mode approximation is crucial: the proper treatment has to be based on cavity QED, 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.