  Previously, we had proposed the technique of light shift imbalance induced
blockade which leads to a condition where a collection of non-interacting atoms
under laser excitation remains combined to a superposition of the ground and
the first excited states, thus realizing a collective state quantum bit which
in turn can be used to realize a quantum computer. In this paper, we show first
that the light shift imbalance by itself is actually not enough to produce such
a blockade, and explain the reason why the limitation of our previous analysis
had reached this constraint. We then show that by introducing Rydberg
interaction, it is possible to achieve such a blockade for a wide range of
parameters. Analytic arguments used to establish these results are confirmed by
numerical simulations. The fidelity of coupled quantum gates based on such
collective state qubits is highly insensitive to the exact number of atoms in
the ensemble. As such, this approach may prove to be viable for scalable
quantum computing based on neutral atoms.
