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Symmetry

Predication and Photon Statistics of a Three-Level System in the Photon Added Negative Binomial Distribution

Tahani A. Aloafi, Azhari A. Elhag, Taghreed M. Jawa, Neveen Sayed-Ahmed, F. S. Bayones, Jamel Bouslimi, Marín Marín

Published Jan 31, 2022• 1 citation
Publisher

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.

DOI
10.3390/sym14020284

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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.
Abstract In this article, we apply a statistical model for forecasting the quantum entanglement between a two‐qubit and optical field in binomial distribution. We explore the link between the atomic Fisher information, quantum entropy, and the statistical properties of the field. The qubit‐qubit entanglement is investigated through concurrence during the interaction time. The dynamics of the statistical quantities will be forecasted using the time series and neural network models. The effect of the field distribution parameter (number of successes) is examined by the time series models and artificial neural network. We compare the accuracy of both modes from the perspective of the dynamic of the quantum entropy and atomic Fisher information. A statistical description for the data has been obtained and is discussed to show the statistical technique analysis the data of statistical quantities. The results obtained have several applications and are related with quantum statistics and quantum information processing.
In this paper, a quantum scheme for a two-qubit system (2QS) and field initially prepared in the excited negative binomial distribution is presented. The field photon statistics is detected from the evolution of the Mandel parameter, while the evolution of von Neumann entropy detects the nonlocal correlation between the 2QS and radiation field. The concurrence is used to detect the qubit-qubit entanglement during the time evolution. The dynamical properties of single-qubit and two-qubit quantum Fisher information are investigated. We visualize the number of photon excitations on the field in negative binomial states with influence of photon success probability. A connection is provided between the dynamical behaviors of these statistical quantities. We have found that the proposed quantities are strongly influenced by the number of excited photons of the field in negative binomial states and photon success probability.
Objective: The study was conducted to estimate the nonlocal correlation between a single qubit and radiation field initially considered in the excited and nonlinear binomial distribution. Material and method: Explicit forms of the excited and nonlinear binomial states are presented. We investigate the dynamical properties of Wehrl entropy as an indicator of the statistical properties of the radiation field during the time evolution. The non-classicality of the field based on the evolution of Mandel parameter also discussed Results: Results of our study show that the Wehrl entropy, qubit-field entanglement and Mandel parameter at the periodic time are an opposite monotonic behavior. Also, a high amount of the entanglement is reached for a high value of deformation parameter. Finally the statistical properties of the field is Poissonian or sub-Poissonian photon distribution. Conclusion: It is concluded from the study that the Wehrl entropy and Mandel parameter were a good indications of the statistical and dynamical properties of the field during the interaction time.
In the present study, temporal behavior of entanglement between photonic binomial distributions and a two-level atom in a leaky cavity, in equilibrium with the environment at a temperature T, is studied.In this regard, the master equation is solved in the secular approximation for the density matrix, when the initial photonic distribution is binomial, while the atomic states obey the Boltzmann distribution.The atom-photon density matrix so calculated is then used to compute the negativity, as a measure of entanglement.The behavior of atom-photon entanglement is, consequently, determined as a function of time and temperature.To justify the behavior of atom-photon entanglement, moreover, we employ the total density matrix to compute and analyze the time evolution of the initial photonic binomial probability distribution.Our results, along with representative figures reveal that the atomphoton degree of entanglement exhibits oscillations while decaying with time and asymptotically vanishes.It is further demonstrated that an increase in the temperature gives rise to a decrease in the entanglement.The finer characteristics of the temporal behavior of the corresponding probability distribution and, consequently, the atom-photon entanglement is also given and discussed.
We developed a quantum scheme of two atoms (TAs) and field initially in a negative binomial state (NBS). We displayed and discussed the physical implications of the obtained results in terms of the physical parameters of the model. By considering that the TAs were initially prepared in a maximally entangled state, and that the single-mode field was in the NBS, the dynamics of quantum phenomena such TAs-field entanglement, TAs entanglement, and parameter estimation were examined. We found that the quantum quantifiers exhibited randomly quasi-periodic and periodic oscillations that depended on the success probability, photon number transition, and the intensity-dependent coupling effect. Furthermore, we analyzed the connection between the dynamical behavior of the quantifiers. This system can be compared with some other ones that are being discussed in the literature, in order to realize the quantum entanglement, and to control the precision of the parameter estimation.
In this paper, an analytical model for the interaction between a moving -type three-level atom and a two-mode radiation field is presented with two-photon transition and in the intensity-dependent coupling regime. After specifying the initial conditions for the atom and the field, the explicit form of the state vector of the entire system is obtained via the time evolution operator. In order to study the entanglement between subsystems, atom and field, temporal behavior of the von Neumann entropy, as a measure of entanglement, is examined.