Reproducing the effects of quantum deformation in the undeformed Jaynes-Cummings model

In the Jaynes-Cummings (JC) model, the time dependence in the coupling parameter allows changes in the forms of the Rabi oscillations. In the inverse problem approach (IPA), the time-dependent coupling parameter is obtained from the resulting population inversion. In this work, we employ the IPA to obtain a time-dependent coupling that reproduces the effects of $\kappa$-deformation in the population inversion of an undeformed JC. This is relevant because it may pave the way for simulating quantum deformation in the JC model and possibly enable an experimental verification in a setting where the coupling can be precisely controlled.