THERMAL SCIENCE

International Scientific Journal

retracted

ENTANGLEMENT AND GEOMETRIC PHASE OF THE COHERENT FIELD INTERACTING WITH A THREE TWO-LEVEL ATOMS IN THE PRESENCE OF NON-LINEAR TERMS

ABSTRACT
We study the interaction of a three two-level atoms (3-2LA) with a one-mode op­tical coherent field in coherent state in the presence of non-linear Kerr medium. The three atoms are initially prepared in upper and entangled states while the field mode is in a coherent state. The constants of motion, 3-2LA and field density matrix are obtained. The analytic results are employed to perform some investigations of the temporal evolution of the von Neumann entropy as measure of the degree of entanglement between the 3-2LA and optical coherent field. The effect of the detuning and the initial atomic states on the evolution of geometric phase and en­tanglement is analyzed. Also, we demonstrate the link between the geometric phase and non-classical properties during the evolution time. Additionally the effect of detuning and initial conditions on the Mandel parameter is studied. The obtained results are emphasize the impact of the detuning and the initial atomic states of the feature of the entanglement, geometric phase and photon statistics of theoptical coherent field.
Due to the mistake of the Guest Editor in the issue Thermal Science 2020 Volume 24, Issue Suppl. 1, two versions of the same paper have been published, one version before revision and other version after correction according to reviewers comments. Thus, we've retracted this version of the paper. The remaining version is available at following link, along with appropriate Corrigendum.
KEYWORDS
PAPER SUBMITTED: 2020-04-19
PAPER REVISED: 2020-05-17
PAPER ACCEPTED: 2020-05-26
PUBLISHED ONLINE: 2020-10-25
DOI REFERENCE: https://doi.org/10.2298/TSCI20S1039H
CITATION EXPORT: view in browser or download as text file
REFERENCES
  1. Kalaga, J. K., et al., Quantum Correlations and Entanglement in a Model Comprised of a Short Chain of Non-Linear Oscillators, Phys. Rev. A, 94 (2019), 032304
  2. Kay, A., et al., Degree of Quantum Correlation Required to Speed Up a Computation, Phys. Rev. A, 92 (2015), 062329
  3. Sete, E. A., et al., Correlated Spontaneous Emission on the Danube, Journal Mod. Opt., 57 (2010), 1311
  4. Giacobino, E., et al., Quantum Optical Effects in Semiconductor Microcavities, Physique, 3 (2002), 1, pp. 41-52
  5. Tan, S. M., Non-Locality of a Single Photon, Phys. Rev. Lett., 66 (1991), 252
  6. Abdel-Khalek, S., et al., Beam Splitter Entangler for Non-Linear Bosonic Fields, Laser Physics, 22 (2012), 9, pp. 1449-1454
  7. Berrada, K., Beam Splitting and Entanglement Generation: Ex-Cited Coherent States, Quant. Inf. Process., 12 (2013), 1, pp. 69-82
  8. Zheng, S. B., et al., Non-Locality of a Single Photon, Phys. Rev. Lett., 85 (2000), 2392
  9. Shi-Jian G. U., Fidelity approach to quantum phase transitions, Int. J. of Mod. Phy. B, 24 (2010), 23, pp. 4371-4458
  10. Purdy, T. P., et al., Strong Optomechanical Squeezing of Light, Phys. Rev. X, 3 (2013), 031012
  11. Sete, E. A., et al., Light-to-Matter Entanglement Transfer in Optomechanics, JOSA B, 31 (2014), 11, pp. 2821-2828
  12. Gershenfeld, N., et al., Bulk Spin-Resonance Quantum Computation, Science, 275 (1997), 5298, pp. 350-356
  13. Kalaga, J. K., et al., Quantum Steering and Entanglement in Three-Mode Triangle Bose-Hubbard System, Quantum Inf. Process, 16 (2017), 265
  14. Braunstein, S. L., Quantum Computing: Where Do We Want to Go Tomorrow, Wiley-VCH, New York, USA, 1999
  15. Von Neumann, J., Mathematical Foundations of Quantum Mechanics by is an Important Early Work in the Development of Quantum Theory, Princeton University Press, Princeton, N. J. USA, 1932
  16. Obada, A.S.-F., et al., New Features of the Atomic Wehrl Entropy and Its Density in Multi-Quanta Two-Level System, Journal of Physics A, 37 (2004), 25, 6573
  17. Berrada, K., et al., Non-Classical Properties and Purity of a Qubit System in Photon-Added Squeezed Thermal States with Time-Dependent Coupling Effect, Physica E, 84 (2016), Oct., pp. 361-366
  18. Abdel-Khalek, S., et al., Dynamic Properties of Wehrl Information Entropy and Wehrl Phase Distribution for a Moving Four-Level Atom, Journal of Russ. Laser Research, 33 (2012), 6, pp. 547-558
  19. Alsahhaf, M. A., et al., Physical Properties, Field Purity, and Quantum Phase for a Two-Level Atom in Photon-Added Coherent States for the Morse Potential, Joirnal of Russ. Laser Research, 38 (2016), 5, pp. 437-445
  20. Obada, A. S.-F., et al., Effects of Stark Shift and Decoherence Terms on the Dynamics of Phase-Space Entropy of the Multiphoton Jaynes Cummings Model, Physica Scripta, 86 (2012), 055009
  21. Obada, A. S.-F., et al., New Features of a Single-Mode Nonlinear Stark Shift in the Presence of Phase Damping, Optics Communications, 285 (2012), 10-11, pp. 2675-2681
  22. Al Naim, A. F., et al., Entanglement and Physical Attributes of the Interaction between Two SC-Qubits and Thermal Field in the Presence of a Magnetic Field, Microelectronics Journal, 86 (2019), Apr., pp. 15-21
  23. Pancharatnam, S., Generalized Theory of Interference, and Its Applications, Proc. Indian Acad. Sci. A, 44 (1956), Nov., pp. 247-262
  24. Berry, M. V., Quantal Phase Factors Accompanying Adiabatic Changes, Proc. R. Soc. Lond. A, 329 (1984), 45
  25. Abdel-Khalek, S., et al., Geometric Phase of a Moving Three-Level Atom, Optics Commun., 283 (2010), 9, pp. 1826-1831
  26. Tavis, M., et al., Exact Solution for an N-Molecule-Radiation-Field Hamiltonian, Phys. Rev., 170 (1968), 379
  27. Deng, X. J., et al., Entanglement Dynamics of a Double Two-Photon Jaynes-Cummings Model with Kerr-like Medium, Chin. Phys. B, 17 (2008), 3209
  28. Vaglica, A., et al., Irreversible Decay of Non-Local Entanglement Via a Reservoir of a Single Degree of Freedom, Phys. Rev. A, 75 (2007) 062120
  29. Wootters, W. K., Entanglement of Formation of an Arbitrary State of Two Qubits, Phys. Rev. Lett., 80 (1998), 2245
  30. Al Naim, A. F., et al., Entanglement of an su(1, 1) Quantum System Interacting with a Single Two-Level Atom in the Presence of Damping Terms, Journal of Russian Laser Research, 39 (2018), 5, pp. 505-513
  31. Abdel-Khalek, S., et al., Effect of Time Dependent Coupling on the Dynamical Properties of the Non-Local Correlation between Two Three-Level Atoms, Int. J. of Theo. Phys., 56 (2017), 9, pp. 2898-2910
  32. Mandel, L., et al., Optical Coherence and Quantum Optics, Cambridge University Press, Cambridge, USA, 1995
  33. Phoenix, S. J. D., et al., Establishment of an Entangled Atom-Field State in the Jaynes-Cummings Model, Phys. Rev. A, 44 (1991), 6023
  34. Khalil, E. M., et al., Entropic Uncertainty in Two Two-Level Atoms Interacting with a Cavity Field in Presence of Degenerate Parametric Amplifier, Journal Opt. Soc. Am. B, 27 (2010), 2, pp. 266-276
  35. Abdel-Khalek, S., et al., Dynamics of Entanglement between Moving Four-Level Atom and Single Mode Cavity Field, Int. J. of Theo. Phys., 50 (2011), 2, pp. 562-570

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence