This is the first (attempted) claim of polariton condensation. It focuses on the second-order coherence $g^{(2)}$ and convincingly shows that in the regime of superlinear increase of ground state populations, while still retaining strong-coupling (with a small blueshift), coherence decreases from a thermal state towards a coherent state. They conclude that this demonstrates «the quantum phase transition from a classical thermal mixed state to a quantum-mechanical pure state in an exciton polariton system» but concede that «It is still an open question what specific quantum state the condensate falls into» and consider Fock states, coherent states or squeezed states as possible contenders.

The problem of going beyond large population of the ground state is paused since the beginning:

Though the observed first order coherence of atoms is a direct manifesta- tion of the wave nature of matter, only second- order and higher-order coherence functions can distinguish quantum-mechanical pure states

from a classical thermal mixed state

Although they do not go into the details of the mechanism of condensation, they assert that not only interactions, but also a weak repulsion (thanks to spin) is «indispensable»:

This weak repul- sive interaction is indispensable for the for-

mation of exciton or polariton BECs.

They work out in details on evidence that they retain polaritons even at high pumping.

Their main result:

Their main conclusion:

We have obtained evidence for the formation of macroscopic quantum coherence by measuring the time domain of second-order coherence function $g^{(2)}(\tau)$ of the light emitted from the

polaritons