Optical memory based on electromagnetically induced transparency (EIT) in a double-{\Lambda}atomic system provides a convenient way to convert the frequency, bandwidth or polarization of optical pulses by storing in one{\Lambda}channel and retrieving in another.This memory-based optical converter can be used to bridge quantum nodes of different physical properties in a quantum network. However, in real atoms, each energy level usually contains degenerate Zeeman states and this may lead to additional energy loss, as have been discussed in our recent theoretical paper (Phys. Rev. A 100, 063843). Here, we present an experimental study on the efficiency variation in the EIT-memory-based optical polarization conversion in cold cesium atomsunder the Zeeman-state optical pumping. The experimental results support the theoretical predictions. Our works provide quantitative knowledge and physical insight useful to the practical implementation of EIT-memory-based optical converter.
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