Stationary light arises in atomic ensembles with certain energy level
configurations, when two counter-propagating classical drives (lasers) are
applied. Probe light coupled to a different energy level transition than the
classical drives can be completely stopped, while still retaining its light
character. We will be interested in the regime of stationary light, where the
probe light still propagates through the atomic ensemble, but extremely slowly.
In other words, probe field has a very low group velocity, which increases its
interaction time with any optical nonlinearity. The enhancement of the
effective nonlinear strength by stationary light is then used to propose a
two-qubit (controlled-phase) quantum gate for the optical photons, which can in
principle work deterministically. Before discussing stationary light and its
application, we also analyse the different fidelity measures that could be
applied to the proposed gate (and related proposals).