Abstract
Description of states of quantum systems in terms of bivectors (in the general case, polyvectors) is proposed as an alternative to vectors in a Hilbert space. This approach is developed for slow atoms under coherent population trapping conditions (in a dark state). The field of local two-dimensional dark subspaces is naturally associated with a local bivector field. An analysis in terms of bivectors is performed to recover the state of an atom or an atomic ensemble by using the condition for its being in some unknown dark state. This approach exposes natural correlations between atoms. The corresponding many-particle states belong to the class of states with positive partial transpose.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Horodecki, P. Horodecki, and R. Horodecki, quantph/0109124.
J. Schliemann, J. I. Cirac, M. Kuś, et al., Phys. Rev. A 64, 022303 (2001).
R. Paškauskas and L. You, Phys. Rev. A 64, 042310 (2001).
Y. S. Li, B. Zeng, X. S. Liu, and G. L. Long, Phys. Rev. A 64, 054302 (2001).
Yu Shi, Phys. Rev. A 67, 024301 (2003).
G. C. Ghirardi and L. Marinatto, Phys. Rev. A 70, 012109 (2004).
P. Zanardi, Phys. Rev. Lett. 87, 077901 (2001); P. Zanardi, D. A. Lidar, and S. Lloyd, Phys. Rev. Lett. 92, 060402 (2004).
V. Vedral, Central Eur. J. Phys. 2, 289 (2003).
S. Oh and J. Kim, Phys. Rev. A 69, 054305 (2004).
C. Lunkes, Č. Brukner, and V. Vedral, Phys. Rev. A 71, 034309 (2005).
C. Simon, Phys. Rev. A 66, 052323 (2002).
W. Happer, Rev. Mod. Phys. 44, 169 (1972).
T. Ya. Popova, A. K. Popov, S. G. Rautian, and R. I. Sokolovskiĭ, Zh. Éksp. Teor. Fiz. 57, 850 (1969) [Sov. Phys. JETP 30, 466 (1970)].
G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, Nuovo Cimento 36, 5 (1976).
A. Akulshin, A. Celikov, and V. Velichansky, Opt. Commun. 84, 139 (1991).
J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
M. O. Scully, Phys. Rep. 129, 191 (1992).
P. Marte, P. Zoller, and J. L. Hall, Phys. Rev. A. 44, 4118 (1991).
A. Aspect, E. Arimondo, R. Kaiser, et al., Phys. Rev. Lett. 61, 826 (1988).
V. S. Smirnov, A. M. Tumaĭkin, and V. I. Yudin, Zh. Éksp. Teor. Fiz. 96, 1613 (1989) [Sov. Phys. JETP 69, 913 (1989)].
A. Shabani and D. A. Lidar, Phys. Rev. A 72, 042303 (2005).
A. V. Taychenachev, A. M. Tumaikin, and V. I. Yudin, Laser Phys. 2, 575 (1992).
R. Dum and M. Olshanii, Phys. Rev. Lett. 76, 1788 (1996).
P. M. Visser and G. Nienhuis, Phys. Rev. A 57, 4581 (1998).
A. M. Basharov, A. A. Bashkeev, and É. A. Manykin, Zh. Éksp. Teor. Fiz. 127, 536 (2005) [JETP 100, 475 (2005)].
Author information
Authors and Affiliations
Additional information
Original Russian Text © L.V. Il’ichev, 2006, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 129, No. 4, pp. 651–658.
Rights and permissions
About this article
Cite this article
Il’ichev, L.V. Analysis of correlations between atoms in terms of bivectors under coherent population trapping conditions. J. Exp. Theor. Phys. 102, 570–576 (2006). https://doi.org/10.1134/S1063776106040066
Received:
Issue Date:
DOI: https://doi.org/10.1134/S1063776106040066