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Physica A Statistical Mechanics and its Applications

Entanglement evaluation with atomic Fisher information

A.‐S. F. Obada, S. Abdel‐Khalek

Published Oct 18, 2009• 48 citations
Publisher
DOI
10.1016/j.physa.2009.09.015

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Quantum Fisher information to the X states of the collective atom ensemble and the scaled quantum fisher information of the atomic subsystem are evaluated analytically in the Dicke Hamiltonian. Critical behavior of the two kinds of Fisher information are in accordant with the analytical results in the thermodynamic limit. Finite-size scaling is analyzed with the large accessible system size due to the effective technique proposed previously. Scaling exponents of the quantum Fisher information are found.
The present research paper considers a three-level atom (3LA) that interacts with a field mode primarily in a photon-added coherent state of Morse potential (PACSMP). The dynamics of entanglement, the photon statistics, and the quantum Fisher information are investigated. The statistics of field photons are discussed by evaluating the Mandel parameter. We check the influence of the energy dissipation and intensity-dependent function. Finally, we detect the relationship between the entanglement, the field’s nonclassical characteristics, and atomic quantum Fisher information throughout the evolution of time. The findings illustrate the important role of the number of added photons and CSMP in affecting the entanglement’s time evolution, the quantum Fisher information, and the Mandel parameter. Based on the obtained results, we reached significant physical phenomena, including the sudden birth and death of the nonlocal correlation between atom-Morse potential field structures.
An electron in a constant magnetic field has the energy levels known as the Landau levels. One can obtain the corresponding radial wave function in cylindrical polar coordinates (e.g., textbook of Landau & Lifshitz). This system is not explored so far in terms of information-theoretical point of view. We here focus on Fisher information associated with these Landau states specified by the two quantum numbers. Fisher information provides a useful measure of the electronic structure in quantum systems such as hydrogen-like atoms [1,2] and molecules under Morse potentials [3]. We numerically evaluate the generalized Laguerre polynomials contained in the radial wave functions. We report that Fisher information increases linearly with the quantum number n that specifies energy levels, but decreases monotonically with the quantum number m (i.e., the index of the generalized Laguerre polynomial). Also, we present relative Fisher information of the Landau states by setting the lowest Landau state as a reference density. The analytical form is just 4n, which does not depend on the other quantum number m. References: 1. T. Yamano, Relative Fisher information of hydrogen-like atoms, Chem. Phys. Lett. 691 (2018) 1962. T. Yamano, Fisher information of radial wavefunctions for relativistic hydrogenic atoms, Chem. Phys. Lett. 731 (2019) 1366183. T. Yamano, Relative Fisher information for Morse potential and isotropic quantum oscillators, J. Phys. Commun. 2 (2018) 085018