Numerical Investigation of the Geometric Phase and Entropy Squeezing for a Two-Level System in the Presence of Decoherence Terms

Affiliation(s)

1Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Araba; 2Informatics Research Institute, City of Scientific Research and Technology Applications, Alexandria, Egypt.

1Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Araba;2Facluty of Pure and Applied Science, International University of Africa, Khartoum, Sudan..

Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Araba.

1Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Araba; 2Informatics Research Institute, City of Scientific Research and Technology Applications, Alexandria, Egypt.

1Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Araba;2Facluty of Pure and Applied Science, International University of Africa, Khartoum, Sudan..

Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Araba.

Abstract

In this paper, we have presented the numerical investigation of the geometric phase and field entropy squeezing for a two-level system interacting with coherent field under decoherence effect during the time evolution. The effects of the initial state setting and atomic dissipation damping parameter on the evolution of the geometric phase and entropy squeezing have been examined. We have reported some new results related to the periodicity and regularity of geometric phase and entropy squeezing.

Cite this paper

M. Salama, A. Elnubi, S. Abdel-Khalek and M. El-Sayed, "Numerical Investigation of the Geometric Phase and Entropy Squeezing for a Two-Level System in the Presence of Decoherence Terms,"*Journal of Electromagnetic Analysis and Applications*, Vol. 5 No. 9, 2013, pp. 359-365. doi: 10.4236/jemaa.2013.59057.

M. Salama, A. Elnubi, S. Abdel-Khalek and M. El-Sayed, "Numerical Investigation of the Geometric Phase and Entropy Squeezing for a Two-Level System in the Presence of Decoherence Terms,"

References

[1] M. I. I. I. Sergent, M. O. Scully and W. E. Lamb, “Laser Physics,” Adison-Wesley, Reading, 1974.

[2] L. Allen and J. H. Eberly, “Optical Resonance and Two-Level Atoms,” Wiley, New York, 1975.

[3] E. T. Jaynes and F. W. Cummings, “Comparison of Quantum and Semiclassical Radiation Theory with Application to the Beam Maser,” Proceedings of the IEEE, Vol. 51, No. 1 1963, pp. 89-109.
doi:10.1109/PROC.1963.1664

[4] F. W. Cummings, “Stimulated Emission of Radiation in a Single Mode,” Physical Review, Vol. 140, No. 4A, 1965, pp. A1051-A1056. doi:10.1103/PhysRev.140.A1051

[5] M. Tavis and F. W. Cummings, “Approximate Solutions for an N-Molecule-Radiation-Field Hamiltonian,” Physical Review, Vol. 188, No. 2, 1968, pp. 692-695.
doi:10.1103/PhysRev.188.692

[6] J. H. Eberly, N. B. Narozhny and J. J. Sanchez, “Periodic Spontaneous Collapse and Revival in a Simple,” Physical Review Letters, Vol. 44, No. 20, 1980, pp. 1323-1326.
doi:10.1103/PhysRevLett.44.1323

[7] P. L. Knight and P. M. Radmore, “Quantum Origin of Dephasing and Revivals in the Coherent-State Jaynes-Cummings Model,” Physical Review A, Vol. 26, No. 1, 1982, pp. 676-679. doi:10.1103/PhysRevA.26.676

[8] R. R. Puri and G. S. Agarwal, “Finite-Q Cavity Electrodynamics: Dynamical and Statistical Aspects,” Physical Review A, Vol. 35, No. 8, 1987, pp. 3433-3449.
doi:10.1103/PhysRevA.35.3433

[9] S. Abdel-Khalek and T. A. Nofel, “Correlation and Entanglement of a Three-Level Atom Inside Dissipative Cavity,” Physica A, Vol. 390, No. 13, 2011, pp. 2626-2635. doi:10.1016/j.physa.2011.02.030

[10] J. Eiselt and H. Risken, “Quasiprobability Distributions for the Jaynes-Cummings Model with Cavity Damping,” Physical Review A, Vol. 43, No. 1, 1991, pp. 346-360.
doi:10.1103/PhysRevA.43.346

[11] B. Englert G. Naraschewski and M. Schenzle, “Numerical Study of the Effect of Coulomb Repulsion on Resonant Tunneling,” Physical Review B, Vol. 50, No. 4, 1994, pp. 2667-2670. doi:10.1103/PhysRevB.50.2667

[12] S. Pancharatnam, “Generalized Theory of Interference, and Its Applications,” Proceedings of the Indian Academy of Science, Section A, Vol. 44, No. 5, 1956, pp. 247-262.

[13] M. V. Berry, “Quantal Phase Factors Accompanying Adiabatic Changes,” Proceedings of the Royal Society of London, Series A, Vol. 392, No. 1802, 1984, pp. 45-57.
doi:10.1098/rspa.1984.0023

[14] T. F. Jordan, “Berry Phases for Partial Cycles,” Physical Review A, Vol. 38, No. 3, 1988, pp. 1590-1592.
doi:10.1103/PhysRevA.38.1590

[15] J. Samuel and R. Bhandari, “General Setting for Berry’s Phase,” Physical Review Letters, Vol. 60, No. 23, 1988, pp. 2339-2342. doi:10.1103/PhysRevLett.60.2339

[16] M. V. Berry, “The Adiabatic Phase and Pancharatnam’s Phase for Polarized Light,” Journal of Modern Optics, Vol. 34, No. 11, 1987, pp. 1401-1407.
doi:10.1080/09500348714551321

[17] H. Weinfurter and G. Banudrek, “Measurement of Berry’s Phase for Noncyclic Evolution,” Physical Review Letters, Vol. 64, No. 12, 1990, pp. 1318-1321.
doi:10.1103/PhysRevLett.64.1318

[18] Y.-S. Wu and H.-Z. Li, “Observable Effects of the Quantum Adiabatic Phase for Noncyclic Evolution,” Physical Review B, Vol. 38, No. 16, 1988, pp. 11907-11910.
doi:10.1103/PhysRevB.38.11907

[19] V. E. Tarasov, “Quantum Computer with Mixed States and Four-Valued Logic,” Journal of Physics A: Mathematical and General, Vol. 35, No. 25, 2002, pp. 5207-5235. doi:10.1088/0305-4470/35/25/305

[20] K. Berrada, H. Eleuch and Y. Hassouni, “Asymptotic Dynamics of Quantum Discord in Open Quantum Systems,” Journal of Physics B: Atomic Molecular and Optical Physics, Vol. 44, No. 14, 2011, p. 145503.

[21] E. Sjoqvist, A. K. Pati, A. K. Ekert, J. S. Anandan, M. Ericsson, D. K. L. Oi and V. Vedral, “Geometric Phases for Mixed States in Interferometry,” Physical Review Letters, Vol. 85, No. 14, 2000, pp. 2845-2849.
doi:10.1103/PhysRevLett.85.2845

[22] V. Vedral, “Geometric Phases and Topological Quantum Computation,” Journal of Modern Optics, Vol. 47, 2000, pp. 2501-2513.

[23] M. Abdel-Aty, “Cavity QED Nondemolition Measurement Scheme Using Quantized Atomic Motion,” Journal of Optics, Vol. 5, No. 4, 2003, pp. 349-354.

[24] M. Abdel-Aty, S. Abdel-Khalek and A.-S. F. Obada, “Pancharatnam Phase of Two-Mode Optical Fields with Kerr Medium,” Optical Review, Vol. 7, No 6, 2000, pp. 499-504. doi:10.1007/s10043-000-0499-6

[25] G. Wagh and V. C. Rakhecha, “On Measuring the Pancharatnam Phase. II. SU(2) Polarimetry,” Physics Letters A, Vol. 197, No. 2, 1995, pp. 112-115.

[26] J. Lu, “The Geometric Phase in Photon Systems,” European Physical Journal D, Vol. 5, No. 3, 1999, pp. 307-310.

[27] Q. V. Lawande, S. V. Lawande and A. Joshi, “Pancharatnam Phase for a System of a Two-Level Atom Interacting with a Quantized Field in a Cavity,” Physics Letters A, Vol. 251, No. 3, 1999, pp. 164-168.
doi:10.1016/S0375-9601(98)00882-2

[28] Y. Aharonov and J. S. Anandan, “Phase Change during a Cyclic Quantum Evolution,” Physical Review Letters, Vol. 58, No. 16, 1987, pp. 1593-1596.
doi:10.1103/PhysRevLett.58.1593

[29] F. Hongyi and F.Yue “Relationship between Squeezing and Entangled State Transformations,” Journal of Physics A: Mathematical and General, Vol. 36, No. 19, 2003, pp. 5319-5332. doi:10.1088/0305-4470/36/19/309

[30] S. Abdel-Khalek, M. M. A. Ahmed and A.-S. F. Obada, “New Aspects of Field Entropy Squeezing as an Indicator for Mixed State Entanglement in an Effective Two-Level System with Stark Shift,” Chinese Physics Letters, Vol. 28, No. 12, 2011, p. 120305.

[31] M. F. Fang, P. Zhou and S. Swain, “Entropy Squeezing for a Two-Level Atom,” Journal of Modern Optics, Vol. 47, No. 6, 2000, pp. 1043-1053.
doi:10.1080/09500340008233404

[32] Z. Qing-Chun and Z. Shi-Nig, “Entropy Squeezing of The Field Interacting with a Nearly Degenerate V-type,” Chinese Physics Letters, Vol. 14, No. 2, 2005, pp. 0336-0343.

[33] E. H. Kennard, “The Uncertainty Relation for Joint Measurement of Position and Momentum,” Physikalische Zeitschrift, Vol. 44, No. 4-5, 1927, pp. 326-352.
doi:10.1007/BF01391200

[34] W. Beckner, “Inequalities in Fourier Analysis,” Annals of Mathematics, Vol. 102, No. 1, 1975, pp. 159-182.
doi:10.2307/1970980

[35] I. Bialynicki-Birula and Mycielski, “Uncertainty Relations for Information Entropy in Wave Mechanics,” Communications in Mathematical Physics, Vol. 44, No. 2, 1975, pp. 129-132. doi:10.1007/BF01608825