Theory of lifetime of exciton incoherently created below its resonance   frequency by inelastic scattering
  When an exciton in semiconductor is scattered and its energy is decreased far below the resonance energy of the bare exciton state, it has been considered that an exciton-polariton is created immediately by the scattering process, because there is no exciton level at that energy. However, according to the recent time-resolved measurements of P emission originating from inelastic exciton-exciton scattering, it looks rather natural to consider that the exciton-polariton is created in a finite time scale which is restricted by a coherence volume of the exciton after the scattering. In this interpretation, the exciton remains in this time scale far below its resonance energy as a transient state in a series of processes. We propose an expression of the P-emission lifetime depending on the coherence volume of the scattered excitons through the conversion process from them to the polaritons. The coherence volume of the scattered excitons appears in the calculation of the inelastic scattering process on the assumption of a finite coherence volume of the bottleneck excitons.Time-resolved optical-gain measurements could be a way for investigating the validity of our interpretation. 
Motoaki Bamba, Shuji Wakaiki, Hideki Ichida, Kohji Mizoguchi, DaeGwi   Kim, Masaaki Nakayama, and Yasuo Kanematsu
cond-mat.mes-hall physics.optics