Exciton-Population Inversion and Terahertz Gain in Resonantly Excited   Semiconductors
  The build-up of exciton populations in resonantly laser excited semiconductors is studied microscopically. For excitation at the $2s$-exciton resonance, it is shown that polarization with a strict $s$-type radial symmetry can be efficiently converted into an incoherent $p$-type population. As a consequence, inversion between the $2p$ and $1s$ exciton states can be obtained leading to the appearance of significant terahertz gain. 
M. Kira and S.W. Koch