# Uniqueness of the Phase Transition in Many-Dipole Cavity Quantum Electrodynamical Systems

## TL;DR

This paper demonstrates a unique superradiant phase transition in many-dipole cavity QED systems, clarifying the conflicting no-go theorems by emphasizing gauge invariance and the definition of radiation.

## Contribution

It introduces an arbitrary gauge approach to show the existence of a single phase transition and clarifies the role of gauge choice in superradiance in cavity QED.

## Key findings

- A unique phase transition occurs in many-dipole cavity QED systems.
- Gauge choice influences the inclusion of polarisation in the radiative subsystem.
- The paradox of no-go and counter no-go theorems is resolved by different radiation definitions.

## Abstract

The possibility of a superradiant phase transition in light-matter systems is the subject of much debate, due to numerous apparently conflicting no-go and counter no-go theorems. Using an arbitrary gauge approach we show that a unique phase transition does occur in archetypal many-dipole cavity QED systems, and that it manifests unambiguously via a macroscopic gauge-invariant polarisation. We find that the gauge choice controls the extent to which this polarisation is included as part of the radiative quantum subsystem and thereby determines the degree to which the abnormal phase is classed as superradiant. This resolves the long-standing paradox of no-go and counter no-go theorems for superradiance, which are shown to refer to different definitions of radiation.