  Very efficient amplification of light-matter waves (polaritons), that are a
superposition of cavity photons and excitons [1] has recently been
reported[2-11]. The optical gain curve versus the pump power shows a threshold
and then saturates to a maximum value[7,11]. Very recently it has been shown
that this limit-value of gain can be greatly enhanced by increasing the
exciton-photon coupling rate, allowing to approach room temperature
operation11. This anomalous enhancement is in contrast with results from
present theories[12,13] describing the process. Here we clarify the mechanisms
determining gain saturation and explain the observed giant amplification. We
show that this enhancement origins from the non-instantaneous nature of
exciton-exciton collisions in semiconductors[14] due to many-body correlations.
We find that the exciton-photon coupling is able to alter the exciton dynamics
during collisions and hence to modify the coupling mechanism at the basis of
amplification. These results give precise indications to favour room
temperature operation for the realization of all-optical microscopic switches
and amplifiers and demonstrate that exciton-exciton collisions in
semiconductors can be controlled and engineered.
