«In this paper, we would like to propose a mechanism of coherent light emission from a mesoscopic

system, quite different from laser or superradiance.»

Coherent light emission from condensing polaritons. F. Yura and E. Hanamura in Phys. Rev. B 50:15457 (1994).  What the paper says!?

This is, chronologically, the first paper (I know) to propose the principle of a polariton laser. They also appear to be the first to mention the possibility to:

control quantum mechanically and mutually both the electronic system and the radiation field on the same footing within the same space

of the microcavity.

They discuss 1D systems, although with no loss of generality (with some motivations due to imperfections of 2D systems of the time), and consider a small one to quantize the system into four modes (a, b, c and d), which are the four bottomest ones along the dispersion relation:

Their equation of motion is:

where «the phonon-scattering rate $A_{ij}$ is evaluated by the first Born approximation at zero lattice temperature:»

Solving this, they find a competition of the modes with gradual buildup towards the ground state:

They also have a possibly interesting modelization of spectral emission and lifetime (cf. their Eq. (3)) although it seems overall incorrect, as dynamical effects of condensation (such as line narrowing) are not taken into account.

The discussions they make are interesting, being so early:

This should not be called Bose condensation in a strict sense, because our system is one dimensional and consists of stationary flow of polaritons, created from the electron-hole pairs or excitons, towards the lower-energy mode. However, the majority of polaritons occupies a single state, as will be shown, so that we will describe this

as a "condensation of polaritons."