Abstract
We transform the nonlinear interaction between a two-level atom and two-mode fields in a frequencyconverter-type device into an inactivation governed by su(2) Lie algebra operators with phase and coupling depending on time. Under an integrability condition that relates them, we obtain a solution to the wave function. We investigate the effects of the functional dependence of the coupling and the initial state of the two-level atom on atomic inversion, entanglement, atomic variable, and entropy squeezing, as well as the autocorrelation function. The different changes for each of these phenomena are noted and displayed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. A. Mishkin and D. F. Walls, Phys. Rev., 185, 1618 (1969).
G. P. Agrawal and C. L. Agrawal, J. Phys. A: Math. Gen., 7, 607 (1974).
D. F. Walls and R. Barakat, Phys. Rev. A, 1, 446 (1970).
J. Tucker and D. F. Walls, Ann. Phys., NY, 52, 1 (1969).
J. Tucker and D. F. Walls, Phys. Rev., 178, 2036 (1969).
W. H. Louisell, Coupled Mode and Parametric Electronics, Wiley, New York (1960).
S. Kumar and C. L. Mehta, Phys. Rev. A, 21, 1573 (1980).
S. Kumar and C. L. Mehta, Phys. Rev. A, 24, 1460 (1981).
M. S. Abdalla, Int. J. Mod. Phys. B, 16, 2837 (2000).
M. S. Abdalla, Phys. Rev. A, 33, 2870 (1986).
M. S. Abdalla, Phys. Rev. A, 34, 4598 (1986).
C. A. Engelbrecht (Ed.), Lecture Notes in Physics, Springer, Berlin (1982), p. 103.
R. Loudon, The Quantum Theory of Light, Oxford, Clarendon (1983).
C. C. Gerry and P. L. Knight, Introductory Quantum Optics, Cambridge University Press (2005), p. 108, Appendix A.
D. Lass and D. P. DiVincenzo, Phys. Rev. A, 57, 190 (1998).
C. H. Bennett and D. P. DiVincenzo, Nature, 404, 247 (2000).
G. Burkard and G. Loss, Phys. Rev. Lett., 88, 047903 (2002).
H.-P. Breaer, D. Burgarth, and F. Petruccione, Phys. Rev. B, 70, 045323 (2004).
A.S.-Y. Hamdouni and F. Petruccione, Phys. Rev. B, 76, 174306 (2007).
M. S. Abdalla, A. Lashin, and G. Sadek, J. Phys. B: At. Mol. Opt. Phys., 41, 01552 (2008).
F. A. A. El-Orany and M. S. Abdalla, J. Phys. A: Math. Theor., 44, 035302 (2011).
M. S. Abdalla and M. M. A. Ahmed, Opt. Commun., 285, 3578 (2012).
M. S. Abdalla, M. M. A. Ahmed, E. M. Khalil, and A.-S. F. Obada, Prog. Theor. Exp. Phys., 073AOZ (2014); DOI 10.1093/ptep/ptu091.
M. S. Abdalla, M. M. A. Ahmed, E. M. Khalil, and A.-S. F. Obada, J. Rus. Laser Res., 35, 169 (2014).
H. J. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragan, Phys. Rev. Lett., 44, 1323 (1980).
P. Meystre and M. S. Zubairy, Phys. Lett. A, 89, 390 (1982).
J. R. Kuklinski and J. L. Madajczyk, Phys. Rev. A, 37, 3175 (1982).
P. W. Milonni, J. R. Ackerhalt, and H. W. Galbraith, Phys. Rev. Lett., 50, 966 (1983).
P. W. Milonni, J. R. Ackerhalt, and H. W. Galbraith, Phys. Rev. Lett., 51, 1108 (1983).
J. J. Slosser, P. Meystre, and S. L. Braunstein, Phys. Rev. Lett., 39, 934 (1989).
J. J. Slosser and P. Slosser, Phys. Rev. A, 41, 3867 (1990).
J. Gea-Banacloche, Phys. Rev. Lett., 65, 3385 (1990).
J. Gea-Banacloche, Phys. Rev. A, 44, 5913 (1991).
S. Haroche and J. Raimond, Adv. Atom. Mol. Phys., 20, 347 (1985).
P. Filipowicz, P. Meystre, G. Rempe, and H. Walther, Opt. Acta, 32, 1105 (1985).
G. Rempe, F. Schmidt-Kaler, and H Walther, Phys. Rev. Lett., 64, 2783 (1990).
V. V. Dodonov and V. I. Man’ko, Invariant and the Evolution of Nonstationary Quantum Systems, Nova Science, Commack, New York (1989).
V. V. Dodonov and V. I. Man’ko, Phys. Rev. A, 20, 550 (1979).
I. A. Malkin, V. I. Man’ko, and D. A. Trifonov, J. Math. Phys., 14, 576 (1973).
E. Y. C. Lu, Phys. Rev. A, 8, 1053 (1973).
R. K. Colegrave and M. S. Abdalla, J. Phys. A: Math. Gen., 16, 3805 (1983).
F. A. A. El-Orany, J. Mod. Opt., 56, 99 (2009).
Mas-Fa Fang, Peng Zhou, and S. Swaim, J. Mod. Opt., 47, 1043 (2000).
J. Sachez-Ruis, Phys. Lett A, 201, 125 (1995).
J. Sachez-Ruis, Phys. Lett A, 244, 189 (1998).
Author information
Authors and Affiliations
Corresponding author
Additional information
Manuscript submitted by the authors in English first on November 14, 2016 and in final form on December 22, 2016.
Rights and permissions
About this article
Cite this article
Abdalla, M.S., Khalil, E.M. & Obada, AS.F. Time-Dependent Interaction Between a Two-Level Atom and N Two-Level Atoms in Terms of su(2) Lie Algebra. J Russ Laser Res 38, 37–49 (2017). https://doi.org/10.1007/s10946-017-9618-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-017-9618-8