Abstract
We study the time evolution of the total and Pancharatnam phase of four-level atoms in the presence of a one-dimensional photonic-band-gap material. We obtain analytical and numerical results under certain parametric conditions and analyze the effect of a Kerr-like medium and the detuning parameter on the dynamics of the Pancharatnam phase for the initial atomic position. We observe an interesting feature of the Pancharatnam phase for the one-dimensional photonic-band-gap material.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. E. Tarasov, J. Phys. A, 35, 5207 (2002).
T. M. El-Shahat, S. Abdel-Khalek, and A.-S.F. Obada, Chaos, Solitons & Fractals, 26, 1293 (2005).
T. M. El-Shahat, S. Abdel-Khalek, M. Abdel-Aty, and A.-S. F. Obada, J. Mod. Opt., 50, 2013 (2003).
T. M. El-Shahat, S. Abdel-Khalek, M. Abdel-Aty, and A.-S. F. Obada, Chaos, Solitons & Fractals, 18, 289 (2003).
M. Abdel-Aty, S. Abdel-Khalek, and A.-S. F. Obada, Chaos, Solitons & Fractals, 12, 2015 (2001).
E. Sjoqvist, A. K. Pati, A. K. Ekert, et al., Phys. Rev. Lett., 85, 2845 (2000).
V. Vedral, J. Mod. Opt., 47, 2501 (2000).
M. Abdel-Aty, J. Opt. B, 5, 349 (2003).
M. Abdel-Aty, S. Abdel-Khalek, and A.-S. F. Obada, Opt. Rev., 7, 499 (2000).
G. Wagh and V. C. Rakhecha, Phys. Lett. A, 197, I12 (1995).
J. Lu, Eur. Phys. J. D, 5, 307 (1999).
Q. V. Lawande, S. V. Lawande, and A. Joshi, Phys. Lett. A, 251, 164 (1999).
M. Abdel-Aty, Phys. Lett. A, 373, 3572 (2009).
M. A. Bouchene and M. Abdel-Aty, Phys. Rev. A, 79, 055402 (2009).
A. Pati, Int. J. Quantum Inf., 1, 135 (2003).
A. Kamli and M. Babiker, Phys. Rev. A, 62, 043804 (2000).
J. D. Joannoupoulos, R. B. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton Unversity Press, Princeton, NJ (1995).
S. John and J. Wang, Phys. Rev. Lett., 64, 2418 (1990).
S. John and T. Quang, Phys. Rev. A, 50, 1764 (1994).
S.-Y. Zhu, H. Chen, and H. Huange, Phys. Rev. Lett., 79, 205 (1997).
E. Paspalakis and P. L. Knight, Phys. Rev. Lett., 81, 293 (1998).
E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A, 60, R33 (1999).
M. Florescu and S. John, Phys. Rev. A, 64, 033801 (2001).
S. Bougouffa and A. Kamli, J. Opt. B: Quantum Semiclass. Opt., 6, S60 (2004).
M. Abdel-Aty, Appl. Phys. B, 81, 193 (2005).
M. Abdel-Aty, Laser Phys., 16, 1381 (2006).
F. Couny, H. Sabert, P. J. Roberts, et al., Opt. Express, 13, 558 (2005).
J. Samuel and R. Bhandari, Phys. Rev. Lett., 60, 2339 (1988).
M. V. Berry, J. Mod. Opt., 34, 1401 (1987).
M. Ericsson, E. Sjöqvist, J. Brännlud, et al., Phys. Rev. A, 67, 020101R (2003).
Q. Li, L. Gong, and Y. Chen, Opt. Commun., 169, 17 (1999).
M. Abdel-Aty, Appl. Phys. B, 88, 1 (2007).
M. Cottam and D. R. Tilley, Introduction to Surface and Superlatice Excitations, Cambridge Unversity Press, Cambridge, UK (1989).
V. M. Agranovich and D. L. Mills, Surface Polaritons, North-Holland, Amsterdam (1982).
J. A. Kong, Theory of Electromagnetic Waves, Wiley, New York (1975).
S. B. Zheng, Quantum Semiclass. Opt. B, 10, 691 (1998).
R. A. Zait, Opt. Commun., 247, 367 (2005).
S. Pancharatnam, Proc. Indian Acad. Sci. A, 44, 247 (1956).
S. S. Hassan, H. A. Batarfi, and R. K. Bullough, J. Opt. B: Quantum Semiclass. Opt., 2, R35 (2000).
D. Deutsch, Proc. Roy. Soc. London A, 400, 97 (1985).
D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information, Springer, Berlin, Heidelberg, New York (2001).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Abdel-Khalek, S., Berrada, K., El-Saman, Y.S. et al. Pancharatnam and total phases for one-dimensional photonic band gaps. J Russ Laser Res 33, 437–447 (2012). https://doi.org/10.1007/s10946-012-9300-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-012-9300-0