Many-Body Effect and Cooperative Phenomena in High-Density Exciton Systems Driven by Light

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We have presented for the first time the unified theory of luminescence spectra for highly excited electron-hole systems which is applicable both to the electron-hole BCS state and to the exciton BEC state. The multiple Coulomb interaction between electron-hole pairs is taken into account by numerically solving the Bethe-Salpeter equation for electron-hole pair correlation function. The effect of the collective quantum fluctuation associtated with the center-of-mass motion of electron-hole pairs is incorporated by the generalized random-phase approximation. The crossover from the exciton BEC to the electron-hole BCS state clearly manifests itself in the calculated luminescence spectra.We have also investigated photo-generated states in strongly correlated electron systems. We have derived the effective Hamiltonian of the Hubbard model for the multi-photon excited states assuming sufficiently large on-site repulsive Coulomb interaction. We have calculated two-photon excited states for a system with 20 sites in the half-filled case with exactly diagonalizing the effective Hamiltonian. We have found that the correlation function for the d-wave superconductivity has finite values even for large distance. This strongly suggests that the photo-induced superconductivity arises in strongly correlated electron systems.