  Motivated by the evidence in PCCO and NCCO of a magnetic quantum critical
point at which Neel order is destroyed, we study the evolution with doping of
the T=0 quantum phases of the electron doped cuprates. At low doping, there is
a metallic Neel state with small electron Fermi pockets, and this yields a
fully gapped d_{x^2-y^2} superconductor with co-existing Neel order at low
temperatures. We analyze the routes by which the spin-rotation symmetry can be
restored in these metallic and superconducting states. In the metal, the loss
of Neel order leads to a topologically ordered `doublon metal' across a
deconfined critical point with global O(4) symmetry. In the superconductor, in
addition to the conventional spin density wave transition, we find a variety of
unconventional possibilities, including transitions to a nematic superconductor
and to valence bond supersolids. Measurements of the spin correlation length
and of the anomalous dimension of the Neel order by neutron scattering or NMR
should discriminate these unconventional transitions from spin density wave
theory.
