Spontaneous and light induced Bose-Einstein condensation of biexcitons

Three alternative descriptions of the biexciton Bose-Einstein condensation are discussed regarding biexcitons as (i) true bosons; (ii) two-exciton bound states; (iii) quaternions consisting of two electrons and two holes. The light induced biexciton polarization, instabilities of the elementary excitations spectrum and additional corrections to the ground state biexciton energy are revealed.