Theoretical study on memory-based optical converter with degenerate Zeeman states

We present a theoretical study on the efficiency variation of coherent light conversion based on optical memories using the electromagnetically induced transparency (EIT) protocol in an atomic system with degenerate Zeeman states. Based on the Maxwell-Bloch equation, we obtain an approximate analytic solution for the converted light pulses which clarifies that two major factors affecting the efficiency of the converted pulses. The first one is the finite bandwidth effect of the pulses and the difference in the delay-bandwidth product of the writing and reading channel due to the difference in the transition dipole moment. The second one is the mismatch between the stored ground-state coherence and the ratio of the Clebsch-Gordan coefficient for the probe and control transition in the reading channel which results in a non-adiabatic energy loss. To correspond to real experimental conditions, we also perform a numerical calculation of the variation in conversion efficiency versus the Zeeman population distribution under the Zeeman-state optical pumping in storing a $\sigma^{+}$-polarized pulse and retrieving with $\sigma^{-}$ polarization in cesium atoms. Our work provides essential physical insights and quantitative knowledge for the development of a coherent optical converter based on EIT-memory.