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Volumetric Entropy Associated with Short Light Pulses Propagation in Gaseous Media
1  Physics Department, Faculty of Science, Assiut University, Assiut 71516, Egypt. Current address: Bağlar Mahallesi, 31500 Ryhanlı, Hatay, Turkey. Retired.
Academic Editor: Joaquim Ferreira (registering DOI)

One of the fundamental interests in laser pulse propagation through atomic or molecular media relies on the control of propagation in terms of the area of the electric field’s envelope over time. This is meaningful as the initial phases of the atomic dipoles are ignored, and the pulses are kept at resonance with their respective optical transitions. Otherwise, the integrated pulse envelope over time becomes complex. Therefore, the real-valued area is not defined properly. Alternatively, in this short communication, we seek local stabilization of the propagated pulses in terms of volumetric entropy of the Bloch ball. The Bloch ball is formed by an irreducible tonsorial set of the density matrix in the Liouville-space subjected to a trace-metric constraint. The volumetric entropy shows up stabilization for off-resonant propagation. The volumetric entropy displays a space-dependent dip close to resonance. This study proposes supremum and infimum identifiers to quantify the divergence of the upper and lower limits of the integral over the complex envelope of the pulse. The adopted volumetric entropy overcame the implementation of the complex-valued information measure on entropy. We examine our proposed technique through short pulses propagation in duplicated two-level atom media. The extinction of formalism to multilevel atoms and off-resonant polychromatic field excitations are possible through n-dimensional Bloch ball consideration. Moreover, volumetric entropy may quantify propagation with frequency chirping and accounts for shifts due to nearby transitions. In fact, entropy has become an essential mathematical measure in studying information processing and its quantification in communicating atomic channels and networks. In typical light storage and light retrieving experiments, the information written or readout might be complex. The efficiency of restoring is defined through energy demands. Our novel treatment taking into account supremum and infimum of the complex pulse integral leads to cross-modulation effects. Both limits show different stability regions across propagation. Therefore, we provide volumetric entropy as a measure of complex information stability.

Keywords: Information geometry; entropy; Bloch-ball; finite-time stability analysis, and control; integral inequities; complex analysis; propagation; Maxwell-Bloch equations