Non-Hermitian phase transition from a polariton Bose-Einstein condensate to a photon laser. R. Hanai, A. Edelman, Y. Ohashi and P. B. Littlewood in Phys. Rev. Lett. 122:185301 (2019).  What the paper says!?

This page is among our 'okay articles'. It should be further expanded but we hope that it will still be useful in its present stage.

This is a nice paper relating dynamical (driven by pumping and decay, i.e., non-Hermitian) condensation to EP. Being Littlewoody type of people, they use the electron-hole pairs and photons basis, which is however not needed for their mechanism.

From the polariton point of view, they have a nice list of experiments reporting two threshold (second threshold to photon BEC), their Refs. [18-29]. Also on exceptional points [35-43]

The normal-to-lasing transition is associated with breaking a U(1) symmetry, but the polariton BEC is already in a U(1)-broken phase

We find that an exceptional point (EP), where the two solutions coalesce [35–43], may appear due to the non-Hermiticity of the equation of motion. We prove and demonstrate that this is the end point of a first-order-like phase transition line between the two solutions, analogous to a critical point in a liquid-gas phase diagram.

Note the «We prove and demonstrate ...»

This, according to them

provides a possible new interpretation to the second threshold as a signal of a lower to upper branch transition

This is definitely related to the one-atom lasing.