Entanglement Quantifier Based on Atomic Wehrl Entropy for Non-Linear Interaction between a Single Two-Level Atom and SU(1,1) Quantum System

Sayed Abdel-Khalek, Manal Al-Quthami, Mohamed M. A. Ahmed

Mathematics Department, Faculty of Science, Taif University, Taif, KSA.

DOI: 10.4236/jqis.2014.41004                

Abstract

In this paper, we study the dynamics of the atomic inversion, scaled atomic Wehrl entropy and marginal atomic Wehrl density for a single two-level atom interacting with SU(1,1) quantum system. We obtain the expectation values of the atomic variables using specific initial conditions. We examine the effects of different parameters on the scaled atomic Wehrl entropy and marginal atomic Wehrl density. We observe an interesting monotonic relation between the different physical quantities for different values of the initial atomic position and detuning parameter.

Keywords

Scaled Atomic Wehrl Entropy; Atomic Q-Function; Atomic Inversion

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	von Neumann, J. (1955) Mathematical Foundations of Quantum Mechanics. rinceton University Press, Princeton.
[2]	Berrada, K., Fanchini, F. and Abdel-Khalek, S. (2012) Quantum Correlations between Each Qubit in a Two-Atom System and the Environment in Terms of Interatomic Distance. Physical Review A, 85, Article ID: 052315. http://dx.doi.org/10.1103/PhysRevA.85.052315
[3]	Berrada, K., Abdel-Khalek, S. and Obada, A.-S.F. (2012) Quantum Fisher Information for a Qubit System Placed inside a Dissipative Cavity. Physics Letters A, 376, 1412-1416. http://dx.doi.org/10.1016/j.physleta.2012.03.023
[4]	Wisemann, H.M. and Milburn, G.J. (2010) Quantum Measurement and Control. Cambridge University Press, Cambridge.
[5]	Popescu, S. and Rohrlich, D. (1997) Thermodynamics and the Measure of Entanglement. Physical Review A, 56, Article ID: R3319. http://dx.doi.org/10.1103/PhysRevA.56.R3319
[6]	Lopez, C.E., Romero, G., Lastra, F., Solano, E. and Retamal, J.C. (2008) Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems. Physical Review Letters, 101, Article ID: 080503. http://dx.doi.org/10.1103/PhysRevLett.101.080503
[7]	Abdel-Aty, M., Abdalla, M.S. and Obada, A.S.F. (2001) Quantum Information and Entropy Squeezing of a Two-Level Atom with a Non-Linear Medium. Journal of Physics A: Mathematical and General, 34, 9129. http://dx.doi.org/10.1088/0305-4470/34/43/303
[8]	Zhang, J.-S. and Chen, A.-X. (2012) Review of Quantum Discord in Bipartite and Multipartite Systems. Quantum Physics Letters, 1, 69-77.
[9]	Mohamed, A.-B.A. (2013) Quantum Discord and Its Geometric Measure with Death Entanglement in Correlated Dephasing Two Qubits System. Quantum Physics, 1, 1-7.
[10]	Abdel-Aty, M. (2005) Information Entropy of a Time-Dependent Three-Level Trapped Ion Interacting with a Laser Field. Journal of Physics A: Mathematical and General, 38, 8589. http://dx.doi.org/10.1088/0305-4470/38/40/008
[11]	Abdel-Aty, M. (2007) Quantum Information Entropy and Multi-Qubit Entanglement. Progress in Quantum Electronics, 31, 1-49.
[12]	Manue Moya-Cessa, H. and Christodoulides, D.N. (2013) A Simple Way to Reconstruct the Wigner Function. Applied Mathematics & Information Sciences, 7, 839-841. http://dx.doi.org/10.12785/amis/070301
[13]	Gravel, C. (2012) Structure of the Probability Distribution for the GHZ Quantum State under Local von Neumann Measurements. Quantum Physics Letters, 1, 87.
[14]	Ahmed, A.-H.M., Zakaria, M.N. and Metwally, N. (2012) Teleportation in the Presence of Technical Defects in Transmission Stations. Applied Mathematics & Information Sciences, 6, 781.
[15]	Miranowicz, A., Matsueda, H. and Wahiddin, M.R.B. (2000) Classical Information Entropy and Phase Distributions of Optical Fields. Journal of Physics A: Mathematical and General, 33, 5159. http://dx.doi.org/10.1088/0305-4470/33/29/301
[16]	Leonski, W., Miranowicz, A. and Piatek, K. (2003) Classical Information Entropy for Single and Two Mode Quantum Fields. In Nowak, J., Zajac, M. and Masajada, Jan., Eds., Proceedings of the SPIE, 13th Polish-Czech-Slovak Conference on Wave and Quantum Aspects of Contemporary Optics, 21 November 2003, 5259, 37-41. http://dx.doi.org/10.1117/12.545063
[17]	Jex, I. and Orlowski, A. (1994) Wehrl’s Entropy Dynamics in a Kerr-Like Medium. Journal of Modern Optics, 41, 2301. http://dx.doi.org/10.1080/09500349414552151
[18]	El-Barakaty, A., Darwish, M. and Obada, A.-S.F. (2011) Purity Loss for a Cooper Pair Box Interacting Dispersively with a Nonclassical Field under Phase Damping. Applied Mathematics & Information Sciences, 5, 122.
[19]	Abdel-Khalek, S. (2009) Wehrl Entropy and Wehrl Phase Distribution of a Single-Trapped Ion Interacting with a Laser Field. Physica Scripta, 80, Article ID: 045302. http://dx.doi.org/10.1088/0031-8949/80/04/045302
[20]	Abdel-Khalek, S., Khalil, E.M. and Ali, S.I. (2008) Entanglement of a Two-Level Atom Papered in a Finite Trio-Coherent State. Laser Physics, 18, 135-143. http://dx.doi.org/10.1134/S1054660X08020072
[21]	Abdel-Khalek, S. and Obada, A.-S.F. (2010) New Features of Wehrl Entropy and Wehrl PD of a Single Cooper-Pair Box Placed inside a Dissipative Cavity. Annals of Physics, 325, 2542-2549. http://dx.doi.org/10.1016/j.aop.2010.05.011
[22]	Eiselt, J. and Risken, H. (1991) Quasiprobability Distributions for the Jaynes-Cummings Model with Cavity Damping. Physical Review A, 43, 346-360, http://dx.doi.org/10.1103/PhysRevA.43.346
[23]	Walls, D.F. and Millburn, G.J. (1985) Effect of Dissipation on Quantum Coherence. Physical Review A, 31, 2403-2408. http://dx.doi.org/10.1103/PhysRevA.31.2403
[24]	Abdel-Khalek, S., Zidan, N. and Abdel-Aty, M. (2011) Analysis of Mixed State Entanglement with Intrinsic Decoherence. Physica E, 44, 6. http://dx.doi.org/10.1016/j.physe.2011.06.007
[25]	Abdel-Khalek, S. (2007) Atomic Wherl Entropy in a Two-Level Atom Interacting with a Cavity Field. Applied Mathematics & Information Sciences, 1, 53-64.
[26]	Abdel-Khalek, S., Abdel-Hameed, H.F. and Abdel-Aty, M. (2011) Atomic Wehrl Entropy of a Single Qubit System. International Journal of Quantum Information, 9, 967-979. http://dx.doi.org/10.1142/S0219749911007538
[27]	Dermez, R. and Abdel-Khalek, S. (2011) Atomic Wehrl Entropy and Negativity as Entanglement Measures for Qudit Pure States in a Trapped Ion. Journal of Russian Laser Research, 32, 287-297. http://dx.doi.org/10.1007/s10946-011-9215-1
[28]	Abdel-Khalek, S., Khalil, E.M. and Ali, S.I. (2008) Entanglement of a Two-Level Atom Papered in a Finite Trio-Coherent State. Laser Physics, 18, 135-143. http://dx.doi.org/10.1134/S1054660X08020072