Bose–Einstein condensation of microcavity polaritons. V. Savona and D. Sarchi in Phys. Stat. Sol. B 242:2290 (2005).  What the paper says!?

«On the theoretical side, it appears that the microcavity polariton domain is not yet benefitting from the

vast theoretical knowledge that is available in the field of BEC.»

This is an account of the «Bose–Einstein condensation of microcavity polaritons» for a symposium held in honour of Marc Ilegems. It provides a nice overview of the situation at the dawn of polariton condensation, as well as historical snippets. There are some inaccuracies in the description, for intance Pau et al. do not claim BEC in their paper (but merely the "boser" effect) and the first theoretical proposal is not by A. Ĭmamoḡlu but by F. Yura & E. Hanamura (which are not cited).

As an historical testimony of note, we find the idea of polariton BEC attributed to C. Weisbuch:

It was back in 1995, sitting right in Marc Ilegems office, that Claude Weisbuch asked: “Do you think they might condense?”. The question was about exciton polaritons in semiconductor planar microcavities

(MCs) and had tickled Claude’s scientific curiosity since his first observation of strongly coupled polaritons in microcavities, a few years before.

This is written before the Kazprzak paper and the question is still considered open:

And yet, although this idea

has been storming around within the polariton community until present, it was clear from the very beginning that, in one way or another, it was too easy to be true.

Almost, the text says more about Savona's mood than about polaritons:

The initial excitement caused by the light effective mass has finally turned into deception.

There is an interesting discussion of works who made claims before that, including in the bulk:

BEC of bulk polaritons has been postulated by several authors [4, 39, 40]

where

[4] A. Griffin, D. W. Snoke, and S. Stringari (Eds.), Bose–Einstein Condensation (Cambridge University Press, Cambridge, 1995).
[39] E. Hanamura and H. Haug, Phys. Rep. 33, 209 (1977).

[40] C. Comte and P. Nozières, J. Physique (Paris) 43, 1069 (1982).

while for 2D polaritons:

at least three other experiments provided clear evidence of polariton final-state stimulation. These experiments were performed

under nonresonant high-energy excitation in the electron–hole continuum [47–49] or at the upper polariton [50]. The most recent claim of polariton BEC was made by Deng et al. [51, 52].

including those that have been retracted, starting with a note on A. Ĭmamoḡlu's seminal proposal:

Though based on very simple considerations, the work by Imamoglu et al. was the first to address the system of microcavity polaritons and to stress the role played by relaxation and recombination dynamics in the context of polariton

BEC.

Which led to the first claim of polariton BEC ([44] is Ref. ):

Shortly after this work, the first experimental claim of polaritonic BEC in microcavities by Pau

et al. [44] followed. [...]

But:

The first boser experiment was however very controversial and its interpretation was strongly criticized shortly after its publication [45]. The main criticism was that, at the measured density, the exciton binding energy and the polariton Rabi splitting would be at least partially bleached and the system would be more correctly described in terms of a plasma of unbound electron–hole pairs, obeying

Fermi statistics. The nonlinearity would then be explained in terms of a standard laser action. The authors of the first boser experiment finally had to withdraw their initial claim and to revert to a more conventional interpretation [46].

This does not even require interactions and ODLRO:

At the time of the boser controversy, it was generally accepted within the polariton community that the required condition for boser action would be the simultaneous observation

of the polariton energy-momentum dispersion with a finite vacuum field Rabi splitting. This would ensure that the emission actually originated from polaritons undergoing final-state stimulation.

There is also a critics of why the later Deng et al. paper also does not qualify for BEC (according to Savona):

Savona & Sarchi's paper otherwise offers

[...] considerations about what steps are in our opinion still required – in theory as well as in experiments – in order to give a satisfactory answer to Claude’s question.

And their view is that interactions are primordial to claim BEC:

Interactions between particles play an essential role in the physics of BEC (see e.g. the discussion by P. Nozières in [4]). Indeed, when we consider the dynamics of a gas undergoing condensation, particleparticle collisions are required to fill the condensate while emptying the excited states. Another essential aspect is the compressibility of the condensate, which turns out to be zero in the noninteracting case and finite in presence of interactions [7]. A finite compressibility is at the origin of most of BEC physics, in

particular the Bogoliubov energy spectrum, superfluidity, and the collective nature of the excitations.

My own work is criticized for neglecting such interactions:

This approach however, does not account for the important role played by polariton–polariton interaction between condensate and noncondensate, which increases the quantum correlations and produces a scattering into the condensate that gives rise to

the BEC phenomenon.

As are all papers based on Boltzmann equations (although A. Ĭmamoḡlu actually predicts a coherent state):

It is important to remark at this point that neither the suggestion by Imamoglu et al., nor the experiment by Pau et al. ever related BEC to the formation of a complex order parameter and of long range order. The claim of polaritonic BEC was solely based on the idea of population buildup. The polariton photoluminescence spectrum under steady-state nonresonant excitation showed a nonlinear increase of the lower polariton peak as a function of pump intensity, which was interpreted as a population buildup driven by final-state stimulation. The word “boser” was specially created to indicate this phenomenon. It is important to remark at this point that neither the suggestion by Imamoglu et al., nor the experiment by Pau et al. ever related BEC to the formation of a complex order

parameter and of long range order. The claim of polaritonic BEC was solely based on the idea of population buildup.

There is also a nice (brief) overview of the early quantum-field theoretic approaches to the problem.

This argument is seldom made (and would deserve a better understanding):

An advantage of polaritons might be the strongly suppressed polariton-polariton Coulomb interaction, essentially related to the small phase space available due to the light effective mass [77]. Therefore, the

polariton system is much closer to the picture of a weakly interacting Bose gas than other exciton systems

This they got right, already at the time:

In the end, the true motivation of all investigations on polaritonic BEC is the perspective of having a quantum fluid available in an artificial nanostructure at a reasonably high

temperature.