  We report first-principles calculations on the coupling between epitaxial
strain, polarization, and oxygen octahedra rotations in monodomain
(PbTiO$_{3}$)$_{n}$/(SrTiO$_{3}$)$_{n}$ superlattices. We show how the
interplay between (i) the epitaxial strain and (ii) the electrostatic
conditions, can be used to control the orientation of the main axis of the
system. The electrostatic constrains at the interface facilitate the rotation
of the polarization and, as a consequence, we predict large piezoelectric
responses at epitaxial strains smaller than those that would be required
considering only strain effects. In addition, ferroelectric (FE) and
antiferrodistortive (AFD) modes are strongly coupled. Usual steric arguments
cannot explain this coupling and a covalent model is proposed to account for
it. The energy gain due to the FE-AFD coupling decreases with the periodicity
of the superlattice, becoming negligible for $n \ge 3$.
