Quantum phase properties of two-mode Jaynes-Cummings model for Schr\"odinger-cat states: interference and entanglement

In this paper we investigate the quantum phase properties for the coherent superposition states (Schr\"odinger-cat states) for two-mode multiphoton Jaynes-Cummings model in the framework of the Pegg-Barnett formalism. We also demonstrate the behavior of the Wigner ($W$) function at the phase space origin. We obtain many interesting results such as there is a clear relationship between the revival-collapse phenomenon occurring in the atomic inversion (as well as in the evolution of the $W$ function) and the behavior of the phase distribution of both the single-mode and two-mode cases. Furthermore, we find that the phase variances of the single-mode case can exhibit revival-collapse phenomenon about the long-time behavior. We show that such behavior occurs for interaction time several times smaller than that of the single-mode Jaynes-Cummings model.Comment: 23, 8 figure

Mathematical Prospective of Coronavirus Infections in Bahrain, Saudi Arabia and Egypt

In this paper, a mathematical prospective of Coronavirus Infections in Bahrain, Suaidi Arabia and Egypt is considered taking into account the development of the propagation of COVID 19 in Wuhan city, China. The model revealed that the number of actual cases of COVID - 19 in the Kingdom of Bahrain is less than expected by about 21.3 times that of the reported cases in the city of Wuhan, while in the Kingdom of Saudi Arabia it is 141.9 less and in Egypt is less than 808 times. This is may be attributed to several factors including ambient temperature, population density, absolute humidity, lifestyle, physical immunity (type of nutrition), accuracy of measurements and number of tests made and other reasons. Finally, we present the expected behavior of the Coronavirus during the forthcoming period