Deterministic conditional phase gate with Rydberg atoms

One of the most promising ways to implement deterministic quantum conditional gate between individual photons is to use the interaction between the large dipole moments of Rydberg polaritons. The multimode character of pulses imposes constraints on implementation of high fidelity quantum gates. To overcome this problem, we have shown that parallel orientation of the dipoles results in optimum fidelity. Additionally, we also have obtained the analytical form for both the induced phase and the fidelity between polaritons for the case that the length of the interaction region is much greater than the size of the polariton wave packets. We also present the advantages of this proposal over previous approaches.