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A fast laser pulse with a q-deformed hyperbolic function shape is investigated in a Multi-level atomic system. Therefore, we first derive the exact solution of the Bloch equations describing a two-level atom excited by a q-deformed laser pulse with dephasing and time-dependent detuning. Next, we analyze the dynamic of the atomic population inversion at resonance and off-resonance of a Rubidium 87 three-level atom driven by a classical weak field and a strong q-deformed control laser. Finally, in order to get a deeper insight of the probe field’s absorption and dispersion properties, we investigate the coherence’s dependence on the q-deformation. Our work demonstrates that, the dynamic of the atomic system can be fully controlled through the manipulation of the asymmetry scaling parameter q of the q-deformed hyperbolic laser wave-form.

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