Polariton laser: thermodynamics and quantum kinetic theory. G. Malpuech, Y. G. Rubo, F. P. Laussy, P. Bigenwald and A. V. Kavokin in Semicond. Sci. Technol. 18:S395 (2003). What the paper says!?
This article which I co-author overviews i) the basic thermodynamic expectations for polariton condensation based on known formulas established for infinite-lived particles, applied to polaritons taking into account their mass in various materials, and ii) kinematic considerations by upgrading the ground state to a quantum harmonic oscillator in an otherwise Boltzmann equations treatment for the relaxation of the gas. The second part prefigures our Phys. Rev. Lett with Y. Rubo.[1]
It has a nice introduction and overview of previous works. Unfortunately, we do not discuss well the difference between BEC and superfluidity.
The superfluid wavefunction thus has a finite extension in
reciprocal space and consequently is not a BEC wavefunction.
In the first part, the fairly expedient consideration is made that in a system of finite size, the quantization of the sum over the now discrete momenta leads to converging "integrals"
and thus, the rhs sum with $\mu=0$ can be seen as a critical density. This defines a «local quasi-condensation», of sizes taken from 100$\mu m$ (size of the spot) and 1m (infinite size as far as a sample is concerned).
From this, the following "phase-space" plots are computed:
There is a nice descriptions of works suggesting overcoming the bottleneck is possible:
a quadratic dependence of emission on the non-resonant pumping power has been evidenced experimentally in II–VI [18] and III–V [19, 20] microcavities. This proved that other relaxation mechanisms allow some polaritons to cross the bottleneck
region.
Boeuf et al [22] have reported exponentially growing emission intensity versus pumping intensity and have claimed that bosonic stimulation of relaxation to the
ground state takes place in their experiments.
There is also a discussion of H. Deng et al. condensation paper of the time.[2] Our concern then was whether this coherence buildup was spontaneous as oppose to acquired, although the authors address this point in their text.
Deng et al [31] have reported, in a GaAs-based microcavity containing 12 QWs, an increase of coherence of light emitted from a polariton ground state, versus non-resonant pumping intensity. This result, which looks extremely promising, still needs to be carefully understood. An important point is whether the coherence of emission is due to polariton Bose condensation or is just inherited from
the coherence of the pumping laser light.