Abstract
In this paper, a detailed solution to the problem of the interaction of two qubits with the su(1, 1) group is presented in a cavity containing a Kerr-like medium. The entanglement between the two qubits and the su(1, 1) Lee group is measured by using quantum field entropy. The entropy squeezing phenomenon is estimated. The relation between the quantum field entropy and concurrence is discussed. The effective of Kerr medium on the von Neumann entropy, the entanglement between the two qubits as well as the initial quantum states are discussed. Also, squeezing periods are estimated for some initial quantum states. We discover through the results that entanglement and entropy squeezing are influenced by Kerr medium and initial conditions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abdalla, M.S., Obada, A.-S.F., Khalil, E.M., Mohamed, A.-B.A.: Wehrl entropy information and purity of a SC charge qubit interacting with a lossy cavity field. Solid State Commun. 184, 56–62 (2014)
Abdalla, M.S., Khalil, E.M., Obada, A.- S.F.: Quantum effect of the Kerr-like medium in terms of SU(1, 1) Lie group in interaction with a two-level atom. Physica A 466, 44–56 (2017)
Abdel-Aty, M., Obada, A.-S.F.: Engineering entanglement of a general three-level system interacting with a correlated two-mode nonlinear coherent state. Eur. Phys. J. D 23, 155–165 (2003)
Alqannas, Haifa S., Khalil, E.M.: Entanglement and sudden death for a nonlinear two qubit interaction with a single su(1, 1) group. Int. J. Ther. Phys. 56, 2019–2027 (2017)
Barut, A.O., Girardello, L.: New “coherent” states associated with non-compact groups. Commun. Math. Phys. 21, 41–55 (1971)
Brune, M., Raimond, J.M., Goy, P., Davidovich, L., Haroche, S.: Realization of a two-photon maser oscillator. Phys. Rev. Lett. 59, 1899–1902 (1987)
Fisher, R.A.: Proceedings of the Cambridge Philosophical Society 1929, 22, 700 reprinted in Collected Papers of R. A. Fisher, edited by J. H. Bennett (University of Adelaide Press, South Australia) pp. 15–40 (1972)
Gauthier, D.J., Wu, L.Q., Morrin, S.E., Mossberg, T.W.: Realization of a continuous-wave, two-photon optical laser. Phys. Rev. Lett. 68, 464–467 (1992)
Gerry, C.C., Eberly, J.H.: Dynamics of a Raman coupled model interacting with two quantized cavity fields. Phys. Rev. A 42, 6805–6815 (1990)
Gou, S.C.: Quantum behavior of a two-level atom interacting with two modes of light in a cavity. Phys. Rev. A 40, 5116–5128 (1989)
Jaynes, E.T., Cummings, F.W.: Comparison of quantum and classical radiation theories with application to the beam maser. Proc. IEEE 51, 89–109 (1963)
Khalil, E.M.: Influence of the external classical field on the entanglement of a two-level atom. Int. J. Theor. Phys 52, 1122–1131 (2013)
Khalil, E.M., Abdalla, M.S., Obada, A.-S.F.: Pair entanglement of two-level atoms in the presence of a nondegenerate parametric amplifier. J. Phys. B 43, 095507 (2010)
Kim, M.S., Lee, J.Y., Ahn, D., Knight, P.L.: Entanglement induced by a single-mode heat environment. Phys. Rev. A 65, 040101 (2002)
Moya-Cessa, H., Vidiella-Barranco, A.: Interaction of squeezed light with two-level atoms. J. Mod. Opt. 39, 2481–2499 (1992)
Neumann, G.J.V.: Mathematische Grundlagen der Quantenmechanik. Monatsh. f. Mathematik und Physik 40, A31–A32 (1933)
Obada, A.-S.F., Ahmed, M.M.A., Faramawy, F.K., Khalil, E.M.: Entropy and entanglement of the nonlinear Jaynes–Cummings model. Chin. J. Phys. 42, 79–91 (2004)
Obada, A.-S.F., Ahmed, M.M.A., Khalil, E.M., Ali, S.I.: Entangled two two-level atoms interacting with a cavity field in the presence of the stark shift terms. Opt. Commun. 287, 215–223 (2013)
Ozaydin, F.: Phase damping destroys quantum Fisher information of W states. Phys. Lett. A 378, 3161–3164 (2014)
Wheeler, J.A., Zurek, W.H.: Quantum Theory and Measurement. Princeton University Press, New Jersey (1983)
Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)
Acknowledgements
The authors are very grateful to the referees and the editor for their constructive remarks, which have helped to improve the manuscript. Taif University Researchers Supporting Project number (TURSP-2020/17), Taif University, Taif, Saudi Arabia.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Alqannas, H.S., Khalil, E.M. Information entropy and squeezing for a two two-level atom interacting with a nonlinear system. Opt Quant Electron 53, 34 (2021). https://doi.org/10.1007/s11082-020-02721-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-020-02721-x