Quantum memory of single-photon polarization qubits via double electromagnetically induced transparency

We present a theoretical investigation on the quantum memory of photonic polarization qubits via electro-magnetically induced transparency (EIT). The system we consider is a tripod-shaped four-level atomic system working under the condition of a double EIT, by which the storage and retrieval of a single-photon polarization qubit are implemented through the switching off and on of a control laser field, and the storage efficiency and the quantum-state fidelity for qubit memory are both calculated. We show that the optimal optical depth for acquiring the maximum efficiency and maximum fidelity of the qubit memory can be obtained simultaneously, which can be further improved by suppressing the optical absorption and dispersion via the choice of the time duration of the input qubit pulse and the amplitude of the control field. We also carry out a calculation on the quantum memory of a single-photon qudit by considering a multipod-shaped atomic-level configuration. The results reported here are useful for understanding the quantum transmission property of slow lights with multiple components and helpful for experimental realizations of high-quality memory of photonic qubits and qudits.