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# Correlation of Dirac potentials and atomic inversion in cavity quantum electrodynamics

(Submitted on 24 Dec 2009 (v1), last revised 14 Jan 2010 (this version, v3))

Abstract: Controlling atomic inversion in cavity quantum electrodynamics (QED) is necessary by tunning the Pauli matrices, $\{\sigma_{1},\sigma_{2},\sigma_{3}\}$, in the transformations of electromagnetic field potential in one-dimensional stationary Dirac model. It can be done by the use of (Bagrov, Baldiotti, Gitman, and Shamshutdinova) BBGS-Darboux transformations \cite{bagrov14darboux} which can fully control the collapse and revival of \textit{modified} Rabi oscillations which the classical effect of electromagnetic field is taken account. It is shown that the choosing of $\sigma_{1}$ in the transformation generates the parabolic potential causing the total collapse of Rabi oscillations; while $\{\sigma_{2}, \sigma_{3}\}$ yield the harmonic oscillator potentials ensuring the coherence of qubits.

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