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

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 polarization. We find that the gauge choice controls the extent to which this polarization 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.

Figure 1

Second derivative of the normalized ground energy $(N\omega {)}^{-1}{d}^2{G}_s/d{\eta }^2$ plotted for various values of $N$ as a function of $\eta$ found using the multipolar-gauge two-level model (solid curves). A precursor to the discontinuity that locates the phase transition in the limit $N=\infty$ can clearly be seen. The green dotted curves provide exact (gauge-invariant) predictions found without two-level truncation. Agreement already occurs at $N=4$. $\beta =3.3$ and $\mathcal{E}$ is chosen such that ${\omega }_m=\omega$.