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Geometric phase for optical free induction decay. (English) Zbl 1211.81107

Summary: Geometric phase is investigated for optical free induction decay with a modified Bloch equation by establishing in connecting density matrices with nonunit vector ray in a complex projective Hilbert space. Under the limiting of pure state, our approach may give out the Berry phase and Aharonov and Anandan one. Furthermore, by comparing our approach with the kinematic one, we find that, after a suitable modification to the kinematic approach, both differences are very small for the Berry phase of mixed states in the optical free induction decay under the case of quasicyclic evolution.
The relations between the population inversion and geometric phase and between the normalized intensity of the heterodyne beat signal and the geometric one are analyzed in process of optical free induction decay. We find that the population inversion and normalized intensity of signal field are a linear function of the geometric phase, which may be helpful to keep temporal storage of quantum information in a long distance quantum communication by using geometric phase.

MSC:

81V80 Quantum optics
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
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[1] Pancharatnam, S.: Proc. Ind. Acad. Sci. A 44, 1225 (1956)
[2] Berry, M.V.: Proc. R. Soc. A 392, 45 (1984) · Zbl 1113.81306 · doi:10.1098/rspa.1984.0023
[3] Aharonov, Y., Anandan, J.: Phys. Rev. Lett. 58, 1593 (1987) · doi:10.1103/PhysRevLett.58.1593
[4] Wang, Z.S., et al.: Phys. Lett. A 359, 608 (2006) · Zbl 1236.81125 · doi:10.1016/j.physleta.2006.07.071
[5] Wang, Z.S., et al.: Phys. Lett. A 372, 775 (2008) · Zbl 1217.81103 · doi:10.1016/j.physleta.2007.08.042
[6] Suter, D., Mueller, K.T., Pine, A.: Phys. Rev. Lett. 60, 1218 (1988) · doi:10.1103/PhysRevLett.60.1218
[7] Bhandari, R., Samuel, J.: Phys. Rev. Lett. 60, 1211 (1988) · doi:10.1103/PhysRevLett.60.1211
[8] Chiao, R.L., et al.: Phys. Rev. Lett. 60, 1214 (1988) · doi:10.1103/PhysRevLett.60.1214
[9] Tian, M., et al.: Phys. Rev. A 67, 011403(R) (2003) · doi:10.1103/PhysRevA.67.011403
[10] Zanardi, P., Rasetti, M.: Phys. Lett. A 264, 94 (1999) · Zbl 0949.81009 · doi:10.1016/S0375-9601(99)00803-8
[11] Wang, Z.S., et al.: Phys. Rev. A 76, 044303 (2007)
[12] Wang, Z.S.: Phys. Rev. A 79, 024304 (2009)
[13] Wang, Z.S., Liu, G.Q., Ji, Y.H.: Phys. Rev. A 79, 054301 (2009)
[14] Uhlmann, A.: Rep. Math. Phys. 24, 229 (1986) · Zbl 0644.46058 · doi:10.1016/0034-4877(86)90055-8
[15] Samuel, J., Bhandari, R.: Phys. Rev. Lett. 60, 2339 (1988) · doi:10.1103/PhysRevLett.60.2339
[16] Ellinas, D., Dupertuis, S.M., Dupertuis, M.A.: Phys. Rev. A 39, 3228 (1989) · doi:10.1103/PhysRevA.39.3228
[17] Dattoli, G., Mignani, R., Torre, A.: J. Phys. A 23, 5795 (1990) · doi:10.1088/0305-4470/23/24/020
[18] Sjöqvist, E., Pati, A.K., Ekert, A., Anandan, J.S., Ericsson, M., Oi, O.K.L., Vedreal, V.: Phys. Rev. Lett. 85, 2845 (2000) · doi:10.1103/PhysRevLett.85.2845
[19] Carollo, A., Fuentes-Guridi, I., Franca Santos, M., Vedral, V.: Phys. Rev. Lett. 90, 160402 (2003) · Zbl 1267.81180 · doi:10.1103/PhysRevLett.90.160402
[20] Fonseca Romero, K.M., Aguiar, A.C., Thomaz, M.T.: Physica A 307, 142 (2002) · Zbl 0994.82053 · doi:10.1016/S0378-4371(01)00589-1
[21] Nazir, A., Spiller, T.P., Munro, W.J.: Phys. Rev. A 65, 042303 (2003) · doi:10.1146/annurev.physiol.65.042602.105304
[22] Whitney, R.S., Gefen, Y.: Phys. Rev. Lett. 90, 190402 (2003) · Zbl 1267.81183 · doi:10.1103/PhysRevLett.90.190402
[23] De Chiara, G., Palma, M.: Phys. Rev. Lett. 91, 090404 (2003)
[24] Tong, D.M., Sjöqvist, E., Kwek, L.C., Oh, C.H.: Phys. Rev. Lett. 93, 080405 (2004)
[25] Whitney, R.S., et al.: Phys. Rev. Lett. 94, 070407 (2005)
[26] Carollo, A., et al.: Phys. Rev. Lett. 96, 150403 (2006)
[27] Wang, Z.S., et al.: Europhys. Lett. 74, 958 (2006) · doi:10.1209/epl/i2006-10057-1
[28] Wang, Z.S., et al.: Phys. Rev. A 75, 024102 (2006)
[29] Wang, Z.S.: Int. J. Theor. Phys. 48, 2353 (2009) · Zbl 1171.81389 · doi:10.1007/s10773-009-0024-z
[30] Barenco, A., Deutsch, D., Ekert, A., Jozsa, R.: Phys. Rev. Lett. 74, 4083 (1995) · doi:10.1103/PhysRevLett.74.4083
[31] Bennett, C.H., DiVincenzo, D.P.: Nature (Lond.) 404, 247 (2000) · Zbl 1369.81023 · doi:10.1038/35005001
[32] Biolatti, E., Iotti, R.C., Zanardi, P., Rossi, F.: Phys. Rev. Lett. 85, 5647 (2000) · doi:10.1103/PhysRevLett.85.5647
[33] Moiseev, S.A., Arslanov, N.M.: Phys. Rev. A 78, 023803 (2008) · doi:10.1103/PhysRevA.78.023803
[34] Gisin, N., Moiseev, S.A., Simon, C.: Phys. Rev. A 76, 014302 (2007) · doi:10.1103/PhysRevA.76.014302
[35] Staudt, M.U., et al.: Phys. Rev. Lett. 98, 113601 (2007) · doi:10.1103/PhysRevLett.98.113601
[36] Moiseev, S.A., Ham, B.S.: Phys. Rev. A 70, 063809 (2004) · doi:10.1103/PhysRevA.70.063809
[37] Cirac, J.I., Zoller, P., Kimble, H.J., Mabuchi, H.: Phys. Rev. Lett. 78, 3221 (1997) · doi:10.1103/PhysRevLett.78.3221
[38] Duan, L.M., Cirac, J.I., Zoller, P., Polzik, E.S.: Phys. Rev. Lett. 85, 5643 (2000) · doi:10.1103/PhysRevLett.85.5643
[39] Eisaman, M.D., Andre, A., Massou, F., Fleischhauer, M., Zibrov, A.S., Lukin, M.D.: Nature (Lond.) 438, 837 (2005) · doi:10.1038/nature04327
[40] Chaneliere, T., Matsukevich, D., Jenkins, S.D., Lan, S.-Y., Kennedy, T.A.B., Kuzmich, A.: Nature (Lond.) 438, 833 (2005) · doi:10.1038/nature04315
[41] Moiseev, S.A., Tittel, W.: In: Workshop on the Storage and Manipulation of Quantum Information in Optically-Addressed Solids, January 25–27, 2008, Bozeman, Montana
[42] Underwood, M.S., Marzlin, K.-P., Tittel, W.: In: Workshop on the Storage and Manipulation of Quantum Information in Optically-Addressed Solids, January 25–27, 2008, Bozeman, Montana
[43] Friedberg, R., Hartmann, S.R.: Phys. Rev. A 52, 1601 (1995) · doi:10.1103/PhysRevA.52.1601
[44] Toyoda, K., Takahashi, Y., Ishikawa, K., Yabuzaki, T.: Phys. Rev. A 56, 1564 (1997) · doi:10.1103/PhysRevA.56.1564
[45] Foster, K.L., Stenholem, S. Brewer, R.G.: Phys. Rev. 10, 2318 (1974) · doi:10.1103/PhysRevA.10.2318
[46] Godone, A., Micalizio, S., Levi, F., Calosso, C.: Phys. Rev. 74, 043401 (2006)
[47] Brewer, R.G. Shoemaker, R.L.: Phys. Rev. 6, 2001 (1972) · doi:10.1103/PhysRevA.6.2001
[48] DeVoe, R.G., Brewer, R.G.: Phys. Rev. Lett. 50, 1269 (1983) · doi:10.1103/PhysRevLett.50.1269
[49] de Veries, H. Wiersma, D.A.: J. Chem. Phys. 69, 897 (1978) · doi:10.1063/1.436605
[50] Mukunda, N., Simon, R.: Ann. Phys. (N.Y.) 228, 205, 269 (1993) · Zbl 0791.58121 · doi:10.1006/aphy.1993.1093
[51] Simon, B.: Phys. Rev. Lett. 51, 2167 (1983) · doi:10.1103/PhysRevLett.51.2167
[52] Garrison, J.C., Chiao, R.Y.: Phys. Rev. Lett. 60, 165 (1998) · doi:10.1103/PhysRevLett.60.165
[53] Anandan, J.: Phys. Rev. Lett. 60, 2555 (1988) · doi:10.1103/PhysRevLett.60.2555
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