  We propose a concept of a quantum cascade laser based on transitions of
bosonic quasiparticles (excitons and exciton-polaritons) in a parabolic
potential trap in a semiconductor microcavity. This laser would emit terahertz
radiation due to bosonic stimulation of excitonic transitions. Dynamics of a
bosonic cascade is strongly different from the dynamics of a conventional
fermionic cascade laser. We show that populations of excitonic ladders are
parity-dependent and quantized if the laser operates without an external
terahertz cavity.
