  We analyze the operation of quantum gates for neutral atoms with qubits that
are delocalized in space, i.e., the computational basis states are defined by
the presence of a neutral atom in the ground state of one out of two trapping
potentials. The implementation of single qubit gates as well as a controlled
phase gate between two qubits is discussed and explicit calculations are
presented for rubidium atoms in optical microtraps. Furthermore, we show how
multi-qubit highly entangled states can be created in this scheme.
