  We investigate the impact of an electric field on the structure of
ultralong-range polar diatomic Rydberg molecules. Both the s-wave and p-wave
interactions of the Rydberg electron and the neutral ground state atom are
taken into account. In the presence of the electric field the angular degree of
freedom between the electric field and the internuclear axis acquires
vibrational character and we encounter two-dimensional oscillatory adiabatic
potential energy surfaces with an antiparallel equilibrium configuration. The
electric field allows to shift the corresponding potential wells in such a
manner that the importance of the p-wave interaction can be controlled and the
individual wells are energetically lowered at different rates. As a consequence
the equilibrium configuration and corresponding energetically lowest well move
to larger internuclear distances for increasing field strength. For strong
fields the admixture of non-polar molecular Rydberg states leads to the
possibility of exciting the large angular momentum polar states via two-photon
processes from the ground state of the atom. The resulting properties of the
electric dipole moment and the vibrational spectra are analyzed with varying
field strength.
