Abstract
We give a fully analytical description of the dynamics of the quasi-probability distribution (Q-PD) functions for any model describing a single two-level qubit interacting with a field. The Wigner function at time (t = 0) and Q function for a pure state as an initial field state are studied. But, in this paper, the temporal behavior of the Q-PD functions for a coherent superposition state (SS) and a statistical mixture of coherent states (SM) for the interaction between a single ion and laser field are investigated. It is found that, the temporal behavior of the Q-PD functions is in very good agreement with its counterpart for the entanglement. If the curve of the entanglement between the trapped ion (specially for the second red sideband) and laser field are known, we can expect the shape of the Q-PD functions.
Similar content being viewed by others
References
E. P. Wigner, Phys. Rev. 40, 749 (1932); M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984).
K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 264 (1940); Y. Kano, J. Math. Phys. 6, 1913 (1965).
R. J. Glauber, Phys. Rev. Lett. 10, 84 (1963).
K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1882 (1968); Phys. Rev. 177, 1857 (1968).
M. S. Kim, E. Park, P. L. Knight, and H. Jeong, Phys. Rev. A 71, 043805 (2005).
M. Terraneo, B. Georgeot, and D. L. Shepelyansky, Phys. Rev. E 71, 066215 (2005); A. J. Bracken and J. G. Wood, Phys. Rev. A 73, 012104 (2006).
D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Rev. Mod. Phys. 75, 281 (2003).
B. E. King, C. S. Wood, C. J. Myatt, et al., Phys. Rev. Lett. 81, 1525 (1998).
P. Bushev, PhD Thesis (Univ. Innsbruck, 2004), urlheartc704; uibk.ac.at/dissertation/bushev_diss.pdf.
P. Bushev, D. Rotter, A. Wilson, et al., e-print quant-ph/0509125.
J. Janszky and An. V. Vinogradov, Phys. Rev. Lett. 64, 2771 (1990).
V. Buzek, A. Vidiella-Barranco, and P. L. Knight, Phys. Rev. A 45, 6570 (1992).
V. Buzek and P. L. Knight, Opt. Commun. 81, 331 (1991).
A.-S. F. Obada and H. A. Hessian, Int. Mod. Phys. Lett. B 16, 1097 (2002); Int. Mod. Phys. Lett. 17, 1553(E) (2003).
A.-S. F. Obada, H. A. Hessian, and M. Abdel-Aty, Int. J. Quantum Information 3, 591 (2005).
S. Bose, I. Fuentes-Guridi, P. L. Knigt, and V. Vedral, Phys. Rev. Lett. 87, 050401 (2001); Phys. Rev. Lett. 87, 279901(E) (2001).
Tzu-Chieh Wei, Kae Nemoto, M. Paul, et al., Phys. Rev. A 67, 022110 (2003).
V. Buzek and G. Adam, Ann. Phys. 245, 37 (1996); C. M. A. Dantas and B. Baseia, Physica A 265, 176 (1999).
G. Nogues, A. Rauschenbeute, S. Osnaghi, et al., Phys. Rev. A 62, 054101 (2000).
P. Roy, Opt. Commun. 221, 145 (2003).
H. Moya-Cessa, J. Opt. B: Quantum Semiclass. Opt. 5, S339 (2003).
V. Buzek and I. Jex, Opt. Commun. 78, 425 (1990); A. Joshi and R. R. Puri, Phys. Rev. A 45, 5056 (1992).
Mahmoud Abdel-Aty, J. Math. Phys. 44, 1457 (2003).
S. Schneider and G. J. Milburn, Phys. Rev. A 57, 3748 (1998).
B. W. Shore and P. L. Knight, J. Mod. Opt. 40, 1195 (1993).
H. Moya-Cessa and P. L. Knight, Phys. Rev. A 48, 2479 (1993).
S. J. D. Phoenix and P. L. Knight, Ann. Phys. 186, 381 (1988); Phys. Rev. A 44, 6023 (1991); Phys. Rev. Lett. 60, 2833 (1991).
V. Buzek, H. Moya-Cessa, P. L. Knight, and S. J. D. Phoenix, Phys. Rev. A 45, 8190 (1992).
S. J. D. Phoenix and P. L. Knight, J. Opt. Soc. Am. B 7, 116 (1990).
P. L. Knight and B. W. Shore, Phys. Rev. A 48, 642 (1993); V. Buzek and B. Hladky, J. Mod. Opt. 40, 1309 (1993).
Mahmoud Abdel-Aty, Physica A 313, 471 (2002).
D. S. Freitas, A. Vidiella-Barranco, and J.A. Roversi, Phys. Lett. A 249, 275 (1998).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Text © Astro, Ltd., 2008.
Rights and permissions
About this article
Cite this article
Hessian, H.A., Mohamed, A.B.A. Quasi-probability distribution functions for a single trapped ion interacting with a mixed laser field. Laser Phys. 18, 1217–1223 (2008). https://doi.org/10.1134/S1054660X08100204
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1054660X08100204