Abstract
An analysis is made of coherent population trapping as a result of resonant interaction of elliptically polarized light with atoms whose energy levels are degenerate with respect to the projection of the angular momentum and are coupled by a dipole transition. Explicit invariant expressions for dark states are obtained in tensor form for all transitions where population trapping occurs. A correspondence is established between the vector of the elliptic polarization and the pair of associated spinors. It is shown that all dark states can be constructed from these spinors by means of a multiple tensor product. For integer values of the angular momenta of the transitions these constructions reduce to spherical functions of a complex variable. As applications analytic expressions are obtained for the dark magneto-optic and geometric potentials, and the change in their profile with increasing angular momenta is analyzed.
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References
G. Alzetta, A. Cozzini, L. Moi, and G. Orriols, Nuovo Cimento B 36, 5 (1976); E. Arimondo and G. Orriols, Lett. Nuovo Cimento 17, 333 (1976); R. M. Whitley and C. R. Stroud, Phys. Rev. A 14, 1498 (1976).
A. Akulshin, A. Celikov, and V. Velichansky, Opt. Comm. 84, 139 (1991); A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. A 57, 2996 (1998).
M. O. Scully, Phys. Rep. 129, 191 (1992); O. Kocharovskaya, Phys. Rep. 129, 175 (1992); G. G. Padmabandu, G. Welch, I. N. Shubin, et al., Phys. Rev. Lett. 76, 2053 (1996).
A. Aspect, E. Arimondo, R. Kaiser, et al., Phys. Rev. Lett. 61, 826 (1988).
A. M. Tumaikin and V. I. Yudin, Zh. Éksp. Teor. Fiz. 98, 81 (1990) [Sov. Phys. JETP 71, 43 (1990)].
G. Grynberg and J.-Y. Courtois, Europhys. Lett. 27, 41 (1994).
A. Hemmerich, M. Wiedemüller, T. Esslinger, et al., Phys. Rev. Lett. 75, 37 (1995).
N. P. Konopleva, A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, Quantum Semiclassic. Opt. 8, 837 (1996).
P. Marte, P. Zoller, and J. L. Hall, Phys. Rev. A 44, 4118 (1991); C. Valentin and P. Pillet, J. Phys. II 4, 1925 (1994); P. D. Featonby, G. S. Summy, C. L. Webb, et al., Phys. Rev. Lett. 81, 495 (1998).
V. S. Smirnov, A. M. Tumaikin, and V. I. Yudin, Zh. Éksp. Teor. Fiz. 96, 1613 (1989) [Sov. Phys. JETP 69, 913 (1989)].
V. Milner and Y. Prior, Phys. Rev. Lett. 80, 940 (1998).
A. V. Taichenachev, 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).
D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (Nauka, Leningrad, 1975; World Scientific, Singapore, 1988).
N. L. Manakov and A. V. Merem’yanin, Zh. Éksp. Teor. Fiz. 111, 1984 (1997) [JETP 84, 1080 (1997)].
N. Ya. Vilenkin, Special Functions and the Theory of Group Representations (Nauka, Moscow, 1991; American Mathematical Society, Providence, 1968).
A. V. Taichenachev, A. M. Tumaikin, V. I. Yudin, and G. Nienhuis, Zh. Éksp. Teor. Fiz. 114, 125 (1998) [JETP 87, 70 (1998)].
A. V. Taichenachev, A. M. Tumaikin, M. A. Ol’shanyi, and V. I. Yudin, Pis’ma Zh. Éksp. Teor. Fiz. 53, 336 (1991) [JETP Lett. 53, 351 (1991)].
M. A. Ol’shanii and V. G. Minogin, Opt. Commun. 89, 393 (1992).
L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Nauka, Moscow, 1973; Pergamon, Oxford, 1975).
A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, Zh. Éksp. Teor. Fiz. 113, 56 (1998) [JETP 86, 1127 (1998)].
A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Mechanical Action of Light on Atoms (Nauka, Moscow, 1991; World Sci., Singapore, 1991).
A. V. Taichenachev, A. M. Tumaikin, V. I. Yudin, and G. Nienhuis, Zh. Éksp. Teor. Fiz. 108, 415 (1995) [JETP 81, 224 (1995)].
A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, Zh. Éksp. Teor. Fiz. 110, 1727 (1996) [JETP 83, 949 (1996)].
J. Lawall, F. Bardou, B. Saubamea, et al., Phys. Rev. Lett. 73, 1915 (1994); J. Lawall, S. Kulin, B. Saubamea, et al., Phys. Rev. Lett. 75, 4194 (1995).
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Translated from Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Fiziki, Vol. 118, No. 1, 2000, pp. 77–86.
Original Russian Text Copyright © 2000 by Ta\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\)chenachev, Tuma\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\)kin, Yudin.
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Taichenachev, A.V., Tumaikin, A.M. & Yudin, V.I. Elliptic dark states: Explicit invariant form. J. Exp. Theor. Phys. 91, 67–75 (2000). https://doi.org/10.1134/1.1307234
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DOI: https://doi.org/10.1134/1.1307234