  An improved measurement of the electron electric dipole moment (EDM) appears
feasible using ground-state alkali atoms in an atomic fountain in which a
strong electric field, which couples to a conceivable electron dipole moment
(EDM), is applied perpendicular to the fountain axis. In a practical fountain,
the ratio of the atomic tensor Stark shift to the Zeeman shift is a facto
mu~100. We expand the complete time evolution operator in inverse powers of
this ratio; complete results are presented for atoms of total spin F=3, 4, and
5. For a specific set of entangled hyperfine sublevels (coherent states),
potential systematic errors enter only as even powers of 1/mu, making the
expansion rapidly convergent. The remaining EDM mimicking effects are further
suppressed in a proposed double-differential setup, where the final state is
interrogated in a differential laser configuration, and the direction of the
strong electric field also is inverted. Estimates of the signal available at
existing accelerator facilities indicate that the proposed apparatus offers the
potential for a drastic improvement in EDM limits over existing measurements,
and for constraining the parameter space of supersymmetric (SUSY) extensions of
the Standard Model.
