  We analyze the peculiar case where the free carrier absorption arising from
LO phonon absorption-assisted transitions becomes negative and therefore turns
into a gain source for quantum cascade lasers. Such an additional source of
gain exists when the ratio between the electronic and the lattice temperatures
is larger than one, a condition that is usually fulfilled in quantum cascade
lasers. We find a gain of few cm$^{-1}$'s at 200K. We report the development of
a terahertz quantum cascade laser operating in the negative free carrier
absorption regime.
