  We present a self-consistent study of coherently coupled two-component
Bose-Einstein condensates. Finite spin-flipping coupling changes the first
order demixing phase transition for Bose-Bose mixtures to a second order phase
transition between an unpolarized and a polarized state. We analise the
excitation spectrum and the structure factor along the transition for a
homogeneous system. We discuss the main differences at the transition between a
coherent coupled gas and a two-component mixture. We finally study the ground
state when spin-(in)dependent trapping potentials are added to the system,
focusing on optical lattices, which give rise to interesting new
configurations.
