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

TL;DR

This paper demonstrates how to reproduce the effects of quantum deformation in the undeformed Jaynes-Cummings model by using an inverse problem approach to find a suitable time-dependent coupling, potentially aiding experimental simulations.

Contribution

It introduces a method to simulate quantum deformation effects in the JC model through inverse problem techniques, enabling experimental verification.

Findings

Successfully reproduces $ $-deformation effects in population inversion

Provides a framework for simulating quantum deformation in controllable systems

Facilitates experimental testing of quantum deformation phenomena

Abstract

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.