  We investigate the electronic structure and properties of Rydberg atoms
exposed to a magnetic quadrupole field. It is shown that the spatial as well as
generalized time reversal symmetries lead to a two-fold degeneracy of the
electronic states in the presence of the external field. A delicate interplay
between the Coulomb and magnetic interactions in the inhomogeneous field leads
to an unusual weak field splitting of the energy levels as well as complex
spatial patterns of the corresponding spin polarization density of individual
Rydberg states. Remarkably the magnetic quadrupole field induces a permanent
electric dipole moment of the atom.
