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Entanglement and Sudden Death for a Two-Mode Radiation Field Two Atoms

Eman M. A. Hilal1, E. M. Khalil2,3,*, S. Abdel-Khalek2,4

1 Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia
2 Mathematics Department, Faculty of Science, Taif University, Taif City, Saudi Arabia
3 Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt
4 Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt

* Corresponding Author: E. M. Khalil. Email:

Computers, Materials & Continua 2021, 66(2), 1227-1236.


The effect of the field–field interaction on a cavity containing two qubit (TQ) interacting with a two mode of electromagnetic field as parametric amplifier type is investigated. After performing an appropriate transformation, the constants of motion are calculated. Using the Schrödinger differential equation a system of differential equations was obtained, and the general solution was obtained in the case of exact resonance. Some statistical quantities were calculated and discussed in detail to describe the features of this system. The collapses and revivals phenomena have been discussed in details. The Shannon information entropy has been applied for measuring the degree of entanglement (DE) between the qubits and the electromagnetic field. The normal squeezing for some values of the parameter of the field–field interaction is studied. The results showed that the collapses disappeared after the field–field terms were added and the maximum values of normal squeezing decrease when increasing of the field–field interaction parameter. While the revivals and amplitudes of the oscillations increase when the parameter of the field–field interaction increases. Degree of entanglement is partially more entangled with increasing of the field-field interaction parameter. The relationship between revivals, collapses and the degree of entanglement (Shannon information entropy) was monitored and discussed in the presence and absence of the field–field interaction.


Cite This Article

E. M. A. Hilal, E. M. Khalil and S. Abdel-Khalek, "Entanglement and sudden death for a two-mode radiation field two atoms," Computers, Materials & Continua, vol. 66, no.2, pp. 1227–1236, 2021.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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