  The mechanism of second thresholds observed in several experiments is
theoretically revealed by studying the BEC-BCS-laser crossover in
exciton-polariton systems. We found that there are two different types for the
second thresholds; one is a crossover within quasi-equilibrium phases and the
other is into non-equilibrium (lasing). In both cases, the light-induced band
renormalization causes gaps in the conduction and valence bands, which
indicates the exsistence of bound electron-hole pairs in contrast to earlier
expectations. We also show that these two types can be distinguished by the
gain spectra.
