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We study ground-state phase diagrams and excitation spectra of Bose-Bosemixtures in an optical lattice by applying the Gutzwiller approximation to thetwo-component Bose-Hubbard model. A case of equal hoppings and equalintra-component interactions for both components is considered. Due to theexistence of inter-component interaction, there appear several quantum phases,such as the superfluid, paired superfluid, and counterflow superfluid phases.We find that the transition from superfluid (SF) to Mott insulator (MI) witheven filling factors can be of the first order for a wide range of the chemicalpotential. We calculate the excitation spectra as a useful probe to identifythe quantum phases and the SF-to-MI transitions. In the excitation spectra ofthe SF phase, there are two gapless modes and a few gapful modes, whichrespectively correspond to phase and amplitude fluctuations of the orderparameters. At the SF-to-MI transition point, we show that the energy gaps ofcertain amplitude modes reach zero for the second-order transition while theyremain finite for the first-order one. Since the excitation spectrum can bemeasured by the Bragg scattering, we calculate the dynamical structure factorby using the linear response theory. We consider three types of densityfluctuations, and show that the density fluctuations are coupled to differentexcitation branches in different quantum phases.

Bose-Bose mixtures in an optical lattice: First-order superfluid-insulator transition and elementary excitations