# Quantum Features of Atom-Field Systems in the Framework of Deformed Fields
## 1 Introduction  
In almost all the areas of physics, the theory of coherent states (CSs) has been used after [PERSON] first built quantum states which are the closest to replicate the classical behavior [1]. [PERSON] was first to observe the notion of coherence linked to these physical states [2, 3]. Similar states were also reinstated by [PERSON] [4, 5], with a widely accepted view that the CSs are linked to the harmonic oscillators (HOs). Due to their vital characteristics, these CSs were simplified to other quantum systems from either a mathematical or physical perspective [6, 7, 8]. [PERSON] [9] and [PERSON] [10] separately presented CSs linked to any set, not only to the Heisenberg group for an HO. An example of an occurrence of these CSs is the spin coherent states (SCSs) connect with su(2) group. These CSs explain various systems and have several usages in statistical mechanics, quantum optics, and physics of condensed matter [6, 7, 8, 11, 12, 13]. Moreover, the quantum groups have been used as a mathematical explanation of deformed Lie algebras [14] that made the construction of the deformed coherent states (DCSs) possible. The DCSs are presented as the actual expansion of the concept of CS. A general deformation of the Glauber CSs was created [15] as connected to deformed quantum HOs. Similarly, deformation of the SCSs is created as states connected to the deformed spin algebra su\({}_{q}\)(2) [16, 17]. Over the last decades, these DCSs have attracted a great attention due to their potential applications in diverse branches of the physics [18, 19, 20, 21]. It has been shown experimentally that the real lasers, bunched, and antibunched lights provide photon distributions that can be sub-Poissonian or super-Poissonian [22, 23]. On the other hand, there are interesting quantitative effects, and related states that are difficult to be prepared and detected, namely superposition quantum states displaying interference effects [24]. Such states exhibit the surprising results of the superposition principle. Furthermore, superposed and nonlinear CSs can begenerated within the motion of trapped ions [25]. The lights with nonclassicality properties are actually a popular area of research, and scientists are interested in further revealing the fundamental truth of the quantum world. In the Jaynes-Cummings model (JCM) [26], the interaction involving radiation and matter is the most effective and simplest system in quantum optics which explains the interaction of two-level atoms with an electromagnetic field. Mathematically, JCM is well described and can as well be resolved precisely [27]. Furthermore, a recent technological breakthrough that made the production of high-Q cavities possible with a possibility to scientifically understand this relatively ideal system for a Rydberg atom in a superconductor cavity [28]. Therefore, much interest has been given to the investigation of JCM and several fascinating quantum occurrences have been speculated: For example Rabi oscillations [29], revival-collapse phenomena of atomic population inversion [30], photon anti-bunching [31], squeezing of information entropy [32], and the atomic dipoles [33]. Quantum entanglement is the most important aspects that differentiate quantum mechanics from the classical correlative. It is a very important aspect that carries out a significant function in different areas of the quantum information theory, for example, quantum key distribution [34; 35; 36; 37; 38], quantum computing [39] and teleportation [40; 41; 42]. Hence, the classification and the quantification of the quantum entanglement have gained ample interest and became highly researched areas in the last few decades. To measure the entanglement, a series of quantifiers have been suggested, for example, concurrence [43; 44], entanglement of formation [45; 46] and linear entropy [47; 48].