  Using the time-dependent Bogoliubov approach, we study adiabaticity for a
two-component Bose-Einstein condensate in a 3D time-dependent optical lattice
with unit filling, in the superfluid and weakly interacting regime. We show
that raising the lattice potential height can couple the ground state of the
Bogoliubov Hamiltonian to excited states with two quasiparticles of opposite
quasi-momenta. In the symmetric case for interactions and density in the two
components these represent sound waves where the two components oscillate out
of phase. We find an analytic expression of the adiabatic time, its dependence
on the fraction of atoms in each component and its scaling with the system
size.
