Abstract
In this paper, we study the dynamics of entanglement between three-level atom and optical field, initially prepared in the squeezed coherent state. We discuss the dynamical behavior of the geometric phase and entanglement, measured by the von Neumann entropy, with and without rotating wave approximation during the time of evolution. The effect of the squeezing and detuning parameters on the evolution of entanglement and geometric phase will be examined. We find that the squeezing and detuning parameters play a central role on the evolution of the geometric phase and nonlocal correlation between the field and the three-level atom. Moreover, we show that the dynamics of the system in the presence of rotating wave approximation has a richer structure compared with the absence of rotating wave approximation.
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C.H. Bennett, D.P. Divincenzo, Nature 404, 247 (2000)
H. Eleuch, Int. J. Mod. Phys. B 24, 5653 (2010)
S. Abdel-Khalek, Appl. Math. Inf. Sci 1, 53 (2007)
S. Abdel-Khalek, E.M. Khalil, S.I. Ali, Laser Phys. 18, 135 (2008)
C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W.K. Wotters, Phys. Rev. Lett. 70, 1895 (1993)
A.E. Kert, Phys. Rev. Lett. 67, 661 (1991)
L.K. Grover, Phys. Rev. Lett. 79, 325 (1997)
V. Giovannetti, S. Lloyd, L. Macoone, Nature 412, 417 (2001)
R. Dermez, S. Abdel-Khalek, J. of Russ. Laser Res 32, 287 (2011)
T.M. El-Shahat, S. Abdel-Khalek, A.S.F. Obada Chaos, Solitons Fractals 26, 1293 (2005)
S. Abdel-Khalek, Int. J. Quantum Inf 7, 1541 (2009)
W.K. Wootters, Quantum Inf. Comput. 1, 27 (2001)
S. Abdel-Khalek, Open Systems Inf. Dynamics 22, 1550015 (2015)
C.H. Bennett, H.J. Bernstein, S. Popescu, B. Schumacher, Physi. Rev. A 53, 2046 (1996)
S. Popescu, D. Rohrlich, Phys. Rev. A 56, R3319 (1997)
K. Zyczkowski, P. Horodecki, A. Sanpera, M. Lewenstein, Phys. Rev. A 58, 883 (1998)
G. Vidal, R.F. Werner, Phys. Rev. A 65, 032314 (2002)
K. Berrada, M. El Baz, H. Eleuch, Y. Hassouni, Int. J. Mod. Phys. C 21, 291 (2010)
K. Berrada, S. Abdel-Khalek, Phys. E. 44, 628 (2011)
C.C. Gerry, A. Benmoussa, Phys. Rev. A 71, 062319 (2005)
D.F. Walls, Nature 306, 141 (1981)
G.J. Milburn, D.F. Walls, M.D. Levenson, J. Opt. Soc. Am. B 1, 390 (1985)
M.D. Ried, D.F. Walls, B.J. Dalton, Phys. Rev. Lett. 55, 1288 (1985)
G.J. Milburn, Opt. Acta 31, 671 (1984)
G.J. Milburn, J. Phys. A 17, 737 (1984)
R.M. Shelby, M.D. Levenson, S.H. Perlmutter, R.G. DeVoe, D.F. Walls, Phys. Rev. Lett. 57, 691 (1986)
C.M. Caves, Phys. Rev. D 23, 1693 (1981)
J. H. Shapiro, H. P. Yuen and J. H. Machado Mata, IEEE Trans. Inf. Theory, 179 (1979)
J. Plebanski, Phys. Rev. 101, 1825 (1956)
W.H. Louisell, Quantum Statistical Properties of Radiation (John Wiley and Sons, New York, 1973)
R.R. Puri, Mathematical Methods of Quantum Optics, Springer Series in Optical Sciences 79, Springer-Verlag, Berlin, (2001)
A.B. Klimov, I. Sainz, S.M. Chumakov, Phys. Rev. A 68, 063811 (2003)
M. Abdel-Aty, J. Opt. B 5, 349 (2003)
H. Eleuch, Y.V. Rostovtsev, M.O. Scully, EPL 89, 50004 (2010)
V.E. Tarasov, J. Phys. A 35, 5207 (2002)
A. Ekert, M. Ericsson, P. Hayden, H. Inamori, J.A. Jones, D.K.L. Oi, V. Vedral, Journal of Mod. Opt. 47(2501) (2000)
V. Vedral, J. Mod. Opt. 47, 2501 (2000)
Y.V. Rostovtsev, H. Eleuch, A. Svidzinsky, H. Li, V. Sautenkov, M.O. Scully, Phys. Rev. A 79, 063833 (2009)
M. Abdel-Aty, S. Abdel-Khalek, A.-S.F. Obada, Opt. Rev. 7, 499 (2000)
G. Wagh, V.C. Rakhecha, Phys. Lett. A 197, I12 (1995)
J. Lu, Eur. Phys. J. D 5, 307 (1999)
Q.V. Lawande, S.V. Lawande, A. Joshi, Phys. Lett. A 251, 164 (1999)
M. Abdel-Aty, Phys. Lett. A 373, 3572 (2009)
M.A. Bouchene, M. Abdel-Aty, Phys. Rev. A 79, 055402 (2009)
A. Pati, Int. J. Quantum Inf 1, 135 (2003)
S. Abdel-Khalek, Quantum Inf. Process 12, 3761 (2013)
M.S. Abdalla, A.S.-F. Obada, S. Abdel-Khalek, Eur. Phys. J. Plus 128, 1 (2013)
S.J. Phoenix, P.L. Knight, Phys. Rev. A 44, 9 (1991)
S. Abdel-Khalek, Y.S. El-Saman, M. Abdel-Aty, Opt. Commun. 283, 1826 (2010)
S. Haifa, Alqannas, S. Abdel-Khalek, J. Russ. Laser Res. 38, 134 (2017)
A. Furusawa, Science 282, 706 (1998)
S. Abdel-Khalek, K. Berrada, S. Alkhateeb, Res. Phys. 6, 780 (2016)
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Abdel-Khalek, S., El-Saman, Y.S., Mechai, I. et al. Geometric Phase and Entanglement of a Three-Level Atom With and Without Rotating Wave Approximation. Braz J Phys 48, 9–15 (2018). https://doi.org/10.1007/s13538-017-0537-5
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DOI: https://doi.org/10.1007/s13538-017-0537-5