Research Article Dynamical Features of Isolated Two- and Three-Level Atoms Interacting with a Cavity Field M. Y. Abd-Rabbou , 1 E. M. Khalil , 2 and Fadhel Almalki 2 1 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, 11884 Cairo, Egypt 2 Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia Correspondence should be addressed to M. Y. Abd-Rabbou; m.elmalky@azhar.edu.eg Received 20 February 2022; Revised 14 June 2022; Accepted 27 June 2022; Published 21 July 2022 Academic Editor: Sandro Wimberger Copyright © 2022 M. Y. Abd-Rabbou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Some dynamical features of two- and three-level atoms interacting locally with an ideal cavity field are investigated. These dynamical features are introduced by employing the statistical atomic inversion, entropy squeezing, and tomographic entropy. Our results show that the initial setting states play an essential role in the temporal evolution of the three quantities. The sensitivity of the two-level atomic state is less than that depicted by the three-level atom. The initial state has a small impact on the two types of entropies for the two-level atom. However, it has an appreciable effect in the case of the three-level atom for different regulations of the initial atomic state. 1. Introduction The interaction between different substances is still a hot topic in quantum optics and information issues. These issues concern the linear atom-field interaction [1] and nonlinear atom-field interaction [2]. The classical simulation of non- linear atom-field interaction in photonic lattices has been realized [3]. In the ultra-strong coupling regime, the quan- tum simulation by applying a rotating wave approximation for the light-matter interaction has been introduced [4]. Some theoretical and practical phenomena of field-atom interaction, such as entanglement, revival, and collapse have been explained [5]. The entanglement of field-field interac- tion has been addressed [6]. Moreover, the effect of cross- Kerr nonlinear on the decoherence of a quantum system was studied [7]. The entanglement of time-dependent atom-atom interaction was discovered [8]. Some conical transformations are used to handle the atom-atom interac- tion with the presence of time dependence. For these inter- actions, some statistical and quantum information has been illustrated to analyze different phenomena [9]. Among these phenomena is the quantum entanglement [10], which is a cornerstone of quantum information theory [11]. Via employing the von Neumann entropy, the degree of entan- glement has been studied for different substances, such as the entanglement of atom-field interaction in resonance and off-resonance cases, has been explored [12]. The degree of entanglement has also been discussed under the Unruh effect, for the two-qubit [13], qubit-qutrit [14], and two- qutrit [15]. Furthermore, the dynamics of entanglement of two isolated Jaynes-Cummings Hamiltonian have been studied, where the first atom interacting only with one cavity field and the second atom interacting with another cavity [16]. In addition, the entanglement of linear atom-field interaction has been illustrated under the influence of Kerr-like medium [17], degenerate parametric amplifier [18], vibrating graphene membrane [19, 20], external classi- cal field [21], damping terms [22], Stark shift terms [23], and deformed cavity field [24]. A double Jaynes-Cummings models in the presence of non-Markovian environments [25], and Kerr medium [26] have been developed to simulate the entanglement dynamics. For high-dimensional atomic Hindawi Advances in Mathematical Physics Volume 2022, Article ID 5258035, 9 pages https://doi.org/10.1155/2022/5258035