Abstract
Consecutive nonlinear optical interactions consisting of two coupled parametric processes, namely, the nondegenerate spontaneous parametric down-conversion and up-conversion, are analyzed. The vacuum state of the input light is considered to be an unstable state decaying into a reservoir of down-converted modes, with one of the modes generated being continuously measured using the up-conversion process. Mean photon numbers at interacting frequencies are studied. Special attention is paid to the case where the nonlinear coupling coefficient for the up-conversion process is much larger than that for the nondegenerate spontaneous parametric down-conversion. It is shown that in this case the result of such consecutive interactions can be interpreted from the viewpoint of the quantum Zeno effect.
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B. Misra and E.C.G. Sudarshan, J. Math. Phys., 18, 756 (1977); C. B. Chiu and E. C. G. Sudarshan, and B. Misra, Phys. Rev. D, 16, 520 (1977).
L. A. Khalfin, Zh. Éksp. Teor. Fiz., 33, 1371 (1957) [Sov. Phys. JETP, 6, 1053 (1958)]; R. G. Winter, Phys. Rev., 123, 1503 (1961).
J. von Neumann, Mathematische Grundlagen der Quantenmechanic, Springer, Berlin (1932); V. B. Braginsky and F. Ya. Khalili, Quantum Measurement, Cambridge University Press (1992).
M. B. Mensky, Quantum Measurements and Decoherence, Kluwer Academic, New York (2000).
R. J. Cook, Phys. Scr. T, 21, 49 (1988).
W. M. Itano, D. J. Heizen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A, 41, 2295 (1990).
A. Luis, Phys. Rev. A, 67, 062113 (2003).
V. Frerichs and A. Schenzle, Phys. Rev. A, 44, 1962 (1991).
M. C. Fischer, B. Gutiérrez-Medina, and M. G. Raizen, Phys. Rev. Lett., 87, 040402 (2001).
P. Facchi and S. Pascazio, Quantum Zeno and Inverse Quantum Zeno Effects, in: E. Wolf (ed.), Progress in Optics, 42, 147 (2001).
S. A. Akhmanov and A. S. Chirkin, Statistical Phenomena in Nonlinear Optics, M. V. Lomonosov Moscow State University (1971) [in Russian]; D. N. Klyshko, Photons and Nonlinear Optics, Gordon & Breach, New York (1988).
A. Luis and J. Pe\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{r}\)ina, Phys. Rev. Lett., 76, 4340 (1996).
K. Thun and J. Pe\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{r}\)ina, Phys. Lett. A, 249, 363 (1998).
J. \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{R}\)ehá\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{c}\)ek, J. Pe\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{r}\)ina, P. Facchi, S. Pascazio, and L. Mi\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{s}\)ta Jr., Phys. Rev. A, 62, 013804 (2000); Opt. Spektroskop., 91, 530 (2001).
A. S. Chirkin, V. V. Volkov, G. D. Laptev, and E. Yu. Morozov, Quantum Electron., 30, 847 (2000).
E. Yu. Morozov and A. S. Chirkin, J. Opt. A: Pure Appl. Opt., 5, 233 (2003).
A. Luis, Phys. Rev. A, 66, 012101 (2002).
A. V. Rodionov and A. S. Chirkin, Opt. Spektroskop., 96, 790 (2004) [Opt. Spectroscop., 96, 721 (2004)].
A. V. Rodionov and A. S. Chirkin, Pisma ZhÉTF, 79, 311 (2004) [JETP Lett., 79, 253 (2004)].
A. Ferraro, M. G. A. Paris, M. Bondani, A. Allevi, E. Puddu, and A. Andreoni, J. Opt. Soc. Am. B, 21, 1241 (2004).
V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Springer, Berlin (1997).
A. S Chirkin and A. V. Nikandrov, J. Opt. B: Quantum Semiclass. Opt., 5, 169 (2003).
M. Bondani, A. Allevi, E. Puddu, A. Andreoni, A. Ferraro, and M. G. A. Paris, Opt. Lett., 29, 180 (2004).
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Chirkin, A.S., Rodionov, A.V. Quantum Zeno effect in two coupled nonlinear optical processes. J Russ Laser Res 26, 83–93 (2005). https://doi.org/10.1007/s10946-005-0008-2
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DOI: https://doi.org/10.1007/s10946-005-0008-2