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.