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Controlling the time evolution of the population of two states in cavityquantum electrodynamics (QED) is necessary by tunning the \textit{modified}Rabi frequency in which the $\textit{extra}$ classical effect ofelectromagnetic field is taken into account.The theoretical explanationunderlying the perturbation of potential on spatial regime of bloch sphere isby the use of (Bagrov, Baldiotti, Gitman, and Shamshutdinova) BBGS-Darbouxtransformations \cite{bagrov14darboux} on the electromagnetic field potentialin one-dimensional stationary Dirac model in which the Pauli matrices are thecentral parameters for controlling the collapse and revival of the Rabioscillations. It is shown that by choosing $\sigma_{1}$ in the transformationgenerates the parabolic potential causing the total collapse of oscillations;while $\{\sigma_{2}, \sigma_{3}\}$ yield the harmonic oscillator potentialsensuring the coherence of qubits.

Correlation of Dirac potentials and atomic inversion in cavity quantum electrodynamics