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Evolution of Population Inversion Controlled by the Time-Dependent Coupling: an Inverse Problem

We propose an inverse idea of controlling the evolution of the population inversion by a time-dependent coupling between the cavity field and a two-level system described through the Jaynes–Cummings model. We demonstrate the detailed procedure by obtaining the population evolution taking the non-sinusoidal form, which is different from the previous sinusoidal Rabi oscillation as the cavity field frequency and coupling parameters are constant during the interaction time.