A Qualitative Perstective on Idempotency Defect of Two Level System Interacting with Laser and Quantized Field

Sayed Abdel-Khalek, Mohammed Mohammed Ahmed, Waleed Nabeel Razek, Abdel Shafy Obada

Mathematics Department, Faculty of Science, Al-Azher University, Nassr City, Cairo, Egypt.
Mathematics Department, Faculty of Science, Al-Azher University, Nassr City, Cairo, Egypt; Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt.
Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia; Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt.
Mathematics Department, Physics Division, National Research Centre, Cairo, Egypt.

DOI: 10.4236/sgre.2010.11006                

Abstract

Entanglement due to the interaction of a two level atom with a laser and quantized field is investigated. The role of the nonlinearity due to these interactions is discussed. It is found that the nonlinearity changes strongly the behavior of the entanglement also the detuning parameters have important role in the structure of the measure of entanglement.

Keywords

Entanglement, Idempotency Defect, Two-Level System, Quantized

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	G. Benenti, G. Casati and G. Strini “Principles of Quan- tum Computation and Information, Vol. 1,” World Scien- tific, 2004.
[2]	C. Bennet, G. Brassard, C. Crepeau, R. Jozsa, A. Peres and W. K. Wootersm, “Teleporting an Unknown Quan- tum State via Dual Classical and Einstein-Podolsky- Rosen Channels,” Physical Review Letter, Vol. 70, No. 1895, 1993.
[3]	A. Ekert, “Quantum Cryptography Based on Bell’s Theorem,” Physical Review Letter, Vol. 67, No. 6, 1991, pp. 661-663.
[4]	L. Ye and G.-C. Guo, “Scheme for Implementing Quan- tum Dense Coding in Cavity QED,” Physical Review Letter A, Vol. 346, No. 5-6, 2005, pp. 330-336.
[5]	O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, N. V. Loock, N. Korolkova and G. Leuchs, “Experiment towards Continu- ous-Variable Entanglement Swapping: Highly Correlated Four-Partite Quantum State,” Physical Review Letter A, Vol. 68, 2003.
[6]	W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Physical Review Letter, Vol. 80, No. 2245, 1998.
[7]	A. Peres, “Separability Criterion for Density Matrices,” Physical Review Letter, Vol. 77, No. 1413, 1996.
[8]	J. von Neumann, “Mathematical Foundations of Quantum Mechanics,” Princeton University Press, Princeton, 1955.
[9]	C. E. Shannon and W. Weaver, “The Mathematical Theory of Communication,” Urbana University Press, Chicago, 1949.
[10]	S. J. D. Phoenix and P. L. Knight, “Fluctuations and Entropy in Models of Quantum Optical Resonance,” Annals of Physics, Vol. 186, No. 381, 1988.
[11]	F. A. A. El-Orany and A.-S. Obada, “On the Evolution of Superposition of Squeezed Displaced Number States with the Multiphoton Jaynes–Cummings Model,” Jounal of Optics B: Quantum Semiclass Optics, Vol. 5, No. 60, 2003.
[12]	M. Lewenstein and T. W. Mossberg, “Spectral and Statistical Properties of Strongly Driven Atoms Coupled to Frequency-Dependent Photon Reservoirs,” Physical Review Letter A, Vol. 37, No. 2048, 1988.
[13]	C. K. Law and J. H. Eberly, “Response of a Two-Level Atom to a Classical Field and a Quantized Cavity Field of Different Frequencies,” Physical Review Letter A, Vol. 43, No. 6337, 1991.
[14]	J. H. Eberly and V. D. Popov, “Phase-Dependent Pump-Probe Line-Shape Formulas,” Physical Review Letter A, Vol. 37, No. 2012, 1988.
[15]	G. M. A. Al-Kader and M. M. A. Ahmad, “On the Interaction of Two-Level Atoms with Squeezed Coherent State,” Chinese Jounal of Physical, Vol. 39, No. 1, 2001.
[16]	A. Ekert and P. L. Knight, “Entangled Quantum Systems and the Schmidt Decomposition,” American Journal of Physics, Vol. 63, No. 415, 1994.