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Abstract
This paper presents a theoretical study of the time-dependent cross-phase-modulation in $^{87}\mathrm{Rb}$. A four-level system in the N configuration is constructed by making use of the hyperfine sublevels present in the rubidium $D$ lines. It is shown that a large transient absorption is present on the electromagnetically induced transparency transition when that field is suddenly turned on. Furthermore, the magnitude and rise time of the cross-phase-modulation are shown to be inversely proportional to each other. We also construct the first-order nonadiabatic corrections to the atomic evolution and demonstrate how these affect slow-light pulse propagation in the atomic ensemble.
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