Abstract
By introducing collective (“cluster”) dynamic variables that explicitly take into account the symmetry of the model Hamiltonians, two new “cluster” (that take into account the quantum mode correlations) types of quasiclassical approximation for the evolution operatorsU H (t) for a wide class of multiphoton scattering models are obtained; the first type treatsU H (t) as the displacement operator of theSU(2)-group with the parameters determined by the solution to the “classical” equations of motion, and the second type gives a spectral expansion ofU H (t) inSU(2)-quasiclassical eigenfunctions. In this framework, an analysis of the dynamics of the most important quantum-statistical characteristics of the models (mean photon numbers and their variances, field quadratures for individual modes, quasiprobability functions, etc.) is given. In particular, the possibility of realization of the two new types of dynamics depending on the initial states (double-periodic harmonic dynamics forSU(2)-coherent initial states and anharmonic dynamics, which leads to such effects as “collapse-revival” of Rabi oscillations, for ordinary coherent states) is revealed.
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N. Bloembergen,Nonlinear Optics, W. A. Benjamin, New York (1965); F. Zernike and J. T. Midwinter,Applied Nonlinear Optics, Wiley, New York (1973); L. D. Landau and E. M. Lifshits,Electrodynamics of Condensed Media [in Russian], Nauka, Moscow, (1982).
J. PerinaQuantum Statistics of Linear and Nonlinear Optical Phenomena, Reidel, Dordrecht (1984); D. N. Klyshko,Physical Fundamentals of Quantum Electronics [in Russian], Nauka, Moscow (1986).
R. Bonifacio and G. Preparata,Phys. Rev. A,2, 336 (1970); S. Kumar and C. L. Mehta,Phys. Rev. A,21, 1573 (1980);24, 1460 (1981).
J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon,Phys. Rev. Lett.,44, 1329 (1980);Phys. Rev. A,23, 236 (1981).
L. Mandel,Opt. Comm.,42, 437 (1982).
S. P. Nikitin and A. V. Masalov,Quantum Opt.,3, 105 (1991).
V. P. Karassiov,Trudy Fizicheskogo Instituta imeni P. N. Lebedeva, Nauka, Moscow (1992), Vol. 208, p. 18 [English translation: “Invariant-algebraic approach to the theory of matter-radiation interaction,” in: V. I. Man'ko and M. A. Markov (eds.),Research in Quantum Field Theory, Proceedings of the Lebedev Physical Institute Nova Science, New York (1996), Vol. 214, p. 1].
S. S. Hassan, M. S. Abdalla, A.-S. F. Obada, et al.,J. Mod. Opt.,40, 1351 (1993).
A. Bandilla, G. Drobny, and I. Jex,Phys. Rev. A,53, 507 (1996).
S. M. Chumakov and M. Kozierowski,Quantum Semiclass. Opt. 8, 775 (1996).
V. P. Karassiov,Teor. Mat. Fiz.,95, 3 (1993);J. Phys. A.,27, 153 (1994).
A. M. Perelomov,Generalized Coherent States and Their Applications [in Russian], Nauka, Moscow (1987) F. T. Arecchi, E. Courtens, R. Gilmore, et al.,Phys. Rev. A,6, 2211 (1972).
V. P. Karassiov, “A nonlinearsl(2)-dynamics and new quasiclassical solutions for a class of coupled systems,” E-print QUANT-PH/9710012 (1997);Phys. Lett. A,238, 19(1998).
E. Jahnke and F. Emde,Funktiontafeln mit Formeln und Kurven, B. E. Teubner, Berlin (1948), 4 Auflag; D. F. Lawden,Elliptic Functions and Applications, Springer Verlag, New York, Berlin (1989).
A. I. Markushevich,Introduction to the Classical Theory, of Abel Functions [in Russian], Nauka, Moscow (1979).
D. Stoler,Phys. Rev. D,1, 3217 (1970).
J. M. Negele,Rev. Mod. Phys.,54, 913 (1982); D. M. Jezek and E. S. Hernandez,Phys. Rev. C,35, 1555, (1987).
A. Erdelyi (ed.),Higher Transcendental Functions. The Bateman Manuscript Project, McGraw-Hill, New York (1953), Vol. 1.
F. A. Berezin,Comm. Math. Phys.,63, 131 (1978); L. G. Yaffe,Rev. Mod. Phys.,54, 407 (1982); A. Chatterjee,Phys. Rep.,186, 249 (1990).
A. Inomata, H. Kuratsuji, and C. C. Gerry,Path Integrals and Coherent States of SU(2)and SU(1,1) World Scientific, Singapore (1992).
M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner,Phys. Rep.,106, 121 (1984).
G. S. Agarwal,Phys. Rev. A,24 2889 (1981);47, 4608 (1993); K. B. Wolf, N. M. Atakishiyev, and S. M. Chumakov, “Wigner distributions of some dynamical models,” in: P. Kasperkovitz and D. Grau (eds.),Proceedings of the Fifth Wigner Symposium (Vienna, August 1997), World Scientific, Singapore (1998), p. 370.
E. Madelung,Die Mathematischen Hilfsmittel des Physikers, Springer Verlag, Berlin (1957).
D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii,Quantum Theory of Angular Momentum [in Russian], Nauka, Leningrad (1975).
B. Yurke and D. Stoler,Phys. Rev. Lett.,57, 13 (1986); G. J. Milburn,Phys. Rev. A,33, 674 (1986); P. Tombesi and A. Mecozzi,J. Opt. Soc. Am. B,4, 1700 (1987)
B. C. Sanders,Phys. Rev. A,40, 2417 (1989); C. C. Gerry and T. Kiefer,J. Phys. A,24, 3513 (1991),
M. M. Sushchinskii,Raman Scattering and the Structure of Matter [in Russian], Nauka, Moscow (1981);Stimulated Light Scattering [in Russian], Nauka, Moscow (1985).
S. A. Akhmanov and N. I. Koroteev,Methods of Nonlinear Optics in the Spectroscopy of Light Scattering [in Russian], Nauka, Moscow (1981).
D. R. Truax,Phys. Rev. D,31, 1988 (1985).
V. P. Karassiov and L. A. Shelepin,Trudy Fizicheskogo Instituta imeni P. N. Lebedeva, Nauka, Moscow (1976), Vol. 87, p. 55 [English translation: “Difference methods and their role in the theory of coherent phenomena,” in: N. G. Basov (ed.),Coherent Cooperative Phenomena, Proceedings of the P. N. Lebedev Physical Institute, Consultants Bureau, New York (1977), Vol. 57, p. 53].
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Translated from a manuscript submitted November 17, 1998.
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Karassiov, V.P. Cluster quasiclassical dynamics in multiphoton scattering models. Analytical results. J Russ Laser Res 20, 239–270 (1999). https://doi.org/10.1007/BF02508543
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DOI: https://doi.org/10.1007/BF02508543