Influence of Frequency-Sweeping on Discrete and Continuous Phase Distributions Generated in Alkali-Metal Vapours

This paper establishes a comparable study on the influence of adiabatic and non-adiabatic pulse excitations for a double-lambda atomic system in alkali metal vapours with a hyperfine structure. Excitation dynamics provided frequency sweeping and emphasized discrete and continuous phase distributions with different excitation schemes of sigmoidal types. The optical pulses are represented by Gaussian or rectangular. We shall focus on the set-up of electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA). The phases of optical fields give similarities to discrete square wave distributions influenced by ramping. We specifically address the population transfer among the hyperfine levels, where the adiabatic condition concerns the density matrix's eigenvalues. During electromagnetically-induced absorption, we found nutation of square wave distributions of the phases for the whole interaction times. Thus, the sensitivity of the double-lambda system to produce large phases are preserved without the need to perform short-cut fields among ground hyperfine levels. The results showed significant control of discrete phase distributions and temporal ramping by sigmoidal membership functions implementation. The relevant equations are the reduced Maxwell equations for the radiation fields, and the density matrix equation in the Liouville space governs the time evolution.