Switch and phase shift of photon polarization qubits via double Rydberg electromagnetically induced transparency

We propose and analyze a scheme for manipulating the propagation of single-photon pulses with two polarization components in a Rydberg atomic gas via double electromagnetically induced transparency. We show that by storing a gate photon in a Rydberg state, a deep and tunable potential for a photon polarization qubit can be achieved based on the strong Rydberg interaction. We also show that the scheme can be used to realize an all-optical switch in the dissipation regime and generate a large phase shift in the dispersion regime for the photon polarization qubit. Moreover, we demonstrate that such a scheme can be utilized to detect weak magnetic fields. The results reported here are not only beneficial for understanding the quantum optical property of Rydberg atomic gases, but also promising for designing devices for quantum information processing.