Photon condensation, Van Vleck paramagnetism, and chiral cavities

Alberto Mercurio, Gian Marcello Andolina, Francesco M. D. Pellegrino, Omar Di Stefano, Pablo Jarillo-Herrero, Claudia Felser, Frank H. L. Koppens, Salvatore Savasta, Marco Polini

Published 2023-02-20Version 1

We introduce a gauge-invariant model of planar, square molecules coupled to a quantized spatially-varying cavity electromagnetic vector potential $\hat{\bm A}({\bm r})$. Specifically, we choose a temporally {\it chiral} cavity hosting a uniform magnetic field $\hat{\bm B}$, as this is the simplest instance in which a transverse spatially-varying $\hat{\bm A}({\bm r})$ is at play. We show that when the molecules are in the Van Vleck paramagnetic regime, an equilibrium quantum phase transition to a photon condensate state occurs.