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<p>Statistical measurements for an optics model containing a five-level atom (5LA) and two quantum systems (2QS) are evaluated into two types of nonlinear Kerr-like media (NKLM). Two quantum systems represent the Boson and SU(1,1) systems. Suggest that the configuration of the 5LA and 2QS is <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13538_2025_1758_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathfrak {X}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">X</mi> </math></EquationSource> </InlineEquation>-type. The 5LA initial state is in excited state as well as the Boson and SU(1,1) quantum systems are in coherent and Barut-Girardello states, respectively. The nonlinear Kerr-like medium represents two different types for two quantum systems. Well-famous statistical measures such as population inversion, Shannon entropy, autocorrelation, coherence, and Cauchy-Schwarz inequality are evaluated and analyzed. The effectiveness of Kerr parameters in the proposed statistical measurements are discussed.</p>

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Effectiveness of Nonlinear Kerr Medium in Statistical Measurements of \(\mathfrak {X}\)-type Five-Level Atom and Two Quantum Systems

  • 期刊论文

  • 发表日期：

    2025年4月22日

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  • Abdallah A. Nahla,
  • M. M. A. Ahmed

摘要

Statistical measurements for an optics model containing a five-level atom (5LA) and two quantum systems (2QS) are evaluated into two types of nonlinear Kerr-like media (NKLM). Two quantum systems represent the Boson and SU(1,1) systems. Suggest that the configuration of the 5LA and 2QS is \(\mathfrak {X}\) X -type. The 5LA initial state is in excited state as well as the Boson and SU(1,1) quantum systems are in coherent and Barut-Girardello states, respectively. The nonlinear Kerr-like medium represents two different types for two quantum systems. Well-famous statistical measures such as population inversion, Shannon entropy, autocorrelation, coherence, and Cauchy-Schwarz inequality are evaluated and analyzed. The effectiveness of Kerr parameters in the proposed statistical measurements are discussed.