  We study ground-state phase diagrams and excitation spectra of Bose-Bose
mixtures in an optical lattice by applying the Gutzwiller approximation to the
two-component Bose-Hubbard model. A case of equal hoppings and equal
intra-component interactions for both components is considered. Due to the
existence 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) with
even filling factors can be of the first order for a wide range of the chemical
potential. We calculate the excitation spectra as a useful probe to identify
the quantum phases and the SF-to-MI transitions. In the excitation spectra of
the SF phase, there are two gapless modes and a few gapful modes, which
respectively correspond to phase and amplitude fluctuations of the order
parameters. At the SF-to-MI transition point, we show that the energy gaps of
certain amplitude modes reach zero for the second-order transition while they
remain finite for the first-order one. Since the excitation spectrum can be
measured by the Bragg scattering, we calculate the dynamical structure factor
by using the linear response theory. We consider three types of density
fluctuations, and show that the density fluctuations are coupled to different
excitation branches in different quantum phases.
