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We propose using coherent optical spectroscopy to study and control optically-forbidden (dark) biexciton states in crystals of cuprous oxide. These states are revealed in the correlation spectra cross resonances due to coherence with the quadrupole allowed 1S exciton manifold. The signal is obtained by means of sum-over-state formalism and comparing equations of motion for the weakly interacting quadrupole excitons with their analogue of non-interacting quasiparticles. The dephasing mechanisms include rapid Auger relaxation of biexcitons which allegedly impedes the Bose-Einstein condensation of quadrupole excitons. An interesting effect attributed to the deviation of the quadrupole excitons from the ortho-para excitons picture is that the positions of the biexciton resonances are defined by the energy splitting between G þ 5;yz and G þ 5;xz excitons and can be tuned by an external perturbation. Possible quantum computing and lasing applications of the quadrupole induced chirality effects of the excitons and biexcitons, and coherence between exciton/biexciton manifolds are discussed. '' Equal parity of the conduction and valence band states produces dipole-forbidden, quadrupole-allowed 1S exciton which is characterized by a long radiative life-time depending on a dominating dephasing mechanism and varies from ns to ps. At low exciton density the measured life-time (%1.7 ns) is determined by phononassisted non-radiative transitions between ortho (J ¼ 1) and optically forbidden para (J ¼ 0) excitons separated by 12 meV due to spin-orbit interaction. Thanks to the small radius, the exciton gas saturation density n s ¼ 10 20 cm À3 is much higher than the critical density n c ¼ 10 17 cm À3 needed for the quadrupole exciton BEC at T ¼ 2 K.Unfortunately, BEC turned out to be an elusive goal due to a strong recombination process that becomes effective at gas densities above %10 14 cm À3 . Usually, this undesirable

The electronic structure of anti-ferromagnetic Cr 2 As is investigated. Anisotropy of exchange interactions between chrome sub-lattices is determined (J X (Cr I −Cr II ) = 4.77meV, J Y (Cr I −Cr II ) = −6.36meV ). The behavior of exchange integrals from magnetic structure is analyzed.