  We investigate the electronic structure and properties of atoms exposed to a
magnetic quadrupole field. The spin-spatial as well as generalized time
reversal symmetries are established and shown to lead to a two-fold degeneracy
of the electronic states in the presence of the field. Low-lying as well as
highly excited Rydberg states are computed and analyzed for a broad regime of
field gradients. The delicate interplay between the Coulomb and various
magnetic interactions leads to complex patterns of the spatial spin
polarization of individual excited states. Electromagnetic transitions in the
quadrupole field are studied in detail thereby providing the selection rules
and in particular the transition wavelengths and corresponding dipole
strengths. The peculiar property that the quadrupole magnetic field induces
permanent electric dipole moments of the atoms is derived and discussed.
