Quantum qubit-optical cavity node: Effects of the temperature and coupling strengths on the cavity Fock-state distribution occupation probability and entropy of the subsystems using Dicke model

One of the most attractive systems for scalable quantum processing is the trapped atom in the optical cavity, which is easily manipulable with lasers. The qubit cavity system represents an attractive structure for quantum optics, with possibilities for applications in quantum detecting, quantum computation, and quantum communication. In addition, the investigation of the cavity-atom system under temperature is a fundamental concept in quantum optics and quantum information science. Here we continue in this quantum way, investigating different qubit(s)-cavity systems (where we increase the numbers of the qubit inside the optical cavity from one to four). Using the Dicke model, we calculate the probability of occupation of the ground state of the cavity $〈{\hat{a}}^{†}\hat{a}〉$ and the expectation values $〈J_z〉$ for each system. We find that these probabilities increase as the coupling strength $C_s$ increases. This leads to reaching the ultra-strong coupling regime, which depends on the number of qubits. To describe the quantum state, we examine the cavity Wigner function WF as a function of the coupling strength $C_s$. Under the same parameters (e.g. $C_s$ and the dissipation rates), we find that the separation of the quantum state in the WFs representation is different from one system to another. Furthermore, since understanding these kinds of systems is very important in order to improve the quantum network system, we study the entropy $S$ of the subsystems (such as $S$ of qubit) in each system. Also, we move beyond by studying the effect of the temperature on the Fock-state distribution occupation probability and entropy of the subsystems. Our results present another step to understanding the qubit(s)-cavity interaction to improve the performance of future quantum networks based on this system. Where the interplay between temperature, coupling strengths, and the Fock-state occupation probabilities contributes significantly to the understanding of quantum decoherence and the thermodynamic properties of quantum systems. Our research on cavity qubit systems is crucial to the development and practical use of quantum networks, which will open the door to distributed quantum computing and other quantum technologies.