  One of the critical elements in the realization of the quantum internet are
deterministic two-photon gates. This $CZ$ photonic gate also completes a set of
universal gates for all-optical quantum information processing. This article
discusses an approach to realize high fidelity $CZ$ photonic gate by storing
both control and target photons within an atomic ensemble using non-Rydberg
electromagnetically induced transparency (EIT) followed by a fast, single-step
Rydberg excitation with global lasers. The proposed scheme operates by relative
intensity modulation of two lasers used in Rydberg excitation. Circumventing
the conventional $\pi$-gap-$\pi$ schemes, the proposed operation features
continuous laser protection of the Rydberg atoms from the environment noise.
The complete spatial overlap of stored photons inside the blockade radius
optimizes the optical depth and simplifies the experiment. The coherent
operation here is performed in the region that was dissipative in the previous
Rydberg EIT schemes. Encountering the main imperfection sources, i.e. the
spontaneous emission of the Rydberg and intermediate levels, population
rotation errors, Doppler broadening of the transition lines, storage/retrieval
efficiency, and atomic thermal motion induced decoherence, this article
concludes that with realistic experimental parameters 99.7\% fidelity is
achievable.
