A non-perturbative no-go theorem for photon condensation in approximate models

Abstract

Equilibrium phase transitions between a normal and a photon condensate state (also known as superradiant phase transitions) are a highly debated research topic, where proposals for their occurrence and no-go theorems have chased each other for the past four decades. Previous nogo theorems have demonstrated that gauge invariance forbids second-order phase transitions to a photon condensate state when the cavity-photon mode is assumed to be spatially uniform. Firstorder phase transitions were previously considered as possible paths to bypass the no-go theorem. In particular, it has been theoretically predicted that a collection of three-level systems coupled to light can display a first-order phase transition to a photon condensate state. Here, we lay down a general no-go theorem, which forbids first-order as well as second-order superradiant phase transitions in a spatially-uniform cavity field. By using the tools of lattice gauge theory, we then derive a fully gaugeinvariant model for three-level systems coupled to light. In agreement with the general theorem, our model does not display photon condensation.

The Jaynes-Cummings model and its descendants

“…In particular, they showed that by disregarding the self-energy term the Hamiltonian is not gauge invariant, see also refs. [72,885] for a recent discussion on the no-go theorem and the importance of gauge invaraince. In sec.…”