Abstract
Statistical and artificial neural network models are applied to forecast the quantum scheme of a three-level atomic system (3LAS) and field, initially following a photon added negative binomial distribution (PANBD). The Mandel parameter is used to detect the photon statistics of a radiation field. Explicit forms of the PANBD are given. The prediction of the Mandel parameter, atomic probability of the 3LAS in the upper state, and von Neumann entropy are obtained using time series and artificial neural network methods. The influence of probability success photons and the number of added photons to the NBD are examined. The total density matrix is used to compute and analyze the time evolution of the initial photonic negative binomial probability distribution that governs the 3LAS-field photon entanglement behavior. It is shown that the statistical quantities are strongly affected by probability success photons and the number of added photons to the NBD. Also, the prediction of quantum entropy is achieved by the time series and neural network.