Entanglement and Fisher Information for Atoms-Field System in the Presence of Negative Binomial States

Kamal Berrada; Sayed Abdel-Khalek; Mariam Algarni; Hichem Eleuch

doi:10.3390/e24121817

Entanglement and Fisher Information for Atoms-Field System in the Presence of Negative Binomial States

Entropy (Basel). 2022 Dec 13;24(12):1817. doi: 10.3390/e24121817.

Authors

Kamal Berrada¹, Sayed Abdel-Khalek^{2

3}, Mariam Algarni⁴, Hichem Eleuch^{5

6

7}

Affiliations

¹ Department of Physics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 5701, Riyadh 11432, Saudi Arabia.
² Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.
³ Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.
⁴ Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.
⁵ Department of Applied Physics and Astronomy, University of Sharjah, Sharjah P.O. Box 27272, United Arab Emirates.
⁶ College of Arts and Sciences, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates.
⁷ Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843, USA.

Abstract

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.

Keywords: atomic systems; binomial distribution; entanglement; negative binomial states; parameter estimation.

Grants and funding

The authors extend their appreciation to the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU) for funding and supporting this work through Research Partnership Program no. RP-21-09-42.