Abstract
We show that quantum optical systems preserving the total number of excitations admit a simple classification of possible resonant transitions (including effective ones), which can be classified by analyzing the free Hamiltonian and the corresponding integrals of motion. Quantum systems not preserving the total number of excitations do not admit such a simple classification, so that an explicit form of the effective Hamiltonian is needed to specify the allowed resonances. The structure of the resonant transitions essentially depends on the algebraic properties of interacting subsystems.
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References
M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics, Springer, Berlin (1990).
V. P. Karassiov, J. Sov. Laser Res., 13, 188 (1992); J. Phys. A: Math. Gen., 27, 153 (1994). B. Abdesselam, J. Beckers, A. Chakrabart, and N. Debergh, J. Phys. A: Math. Gen., 29, 3075 (1996).
J. H. Shirley, Phys. Rev., 138, B797 (1965).
C. Cohen-Tannoudji, J. Dupont-Roc, and C. Fabre, J. Phys. B: At. Mol. Opt. Phys., 6, L214 (1973).
T. Yabuzaki, S. Nakayama, Y. Murakami, and T. Ogawa, Phys. Rev. A, 10, 1955 (1974).
A. Schenzle, Nonlinear Optical Phenomena and Fuctuations, Lecture Notes in Physics, Springer, Berlin (1981), Vol. 155, p. 103. Y. R. Shen, The Principles of Nonlinear Optics, John Wiley, New York (1985). L. A. Lugiato, P. Galatola, and L. M. Narducci, Opt. Commun., 76, 276 (1990). L. Sczaniecki, Phys. Rev. A, 28, 3493 (1983). M. Hillery and L. D. Mlodinow, Phys. Rev. A, 31, 797 (1985). D. J. Klein, J. Chem. Phys., 61, 786 (1974).
A. B. Klimov, I. Sainz, and S. M. Chumakov, Phys. Rev. A, 68, 063811 (2003).
A. B. Klimov, I. Sainz, and C. Saavedra, J. Opt. B: Quantum Semiclass. Opt., 6, 448 (2004).
I. Sainz, A. B. Klimov, and C. Saavedra, Phys. Lett. A, 351, 26 (2006).
R. Dicke, Phys. Rev., 93, 99 (1954). E.T. Jaynes and F. W. Cummings, Proc. IEEE, 51, 89 (1963). B. W. Shore and P. L. Knight, J. Mod. Opt., 40, 1195 (1993).
R. R. Puri and R. K. Boullough, J. Opt. Soc. Am. B, 5, 2021 (1988).
A. B. Klimov and C. Saavedra, Phys. Lett. A, 247, 14 (1998).
F. Bloch and A. Siegert, Phys. Rev., 57, 552 (1940).
A. B. Klimov and L. L. S’anchez-Soto, Phys. Rev. A, 61, 063802 (2000).
A. B. Klimov, L. L. S’anchez-Soto, A. Navarro, and E. C. Yustas, J. Mod. Opt., 49, 2211 (2002).
P. W. Higgs, J. Phys. A: Math. Gen., 12, 309 (1979).
M. Roĉek, Phys. Lett. B, 255, 554 (1991).
D. Bonatsos, C. Daskaloyannis, and G. A. Lalazissis, Phys. Rev. A, 47, 3448 (1993).
E. K. Sklyanin, Funct. Anal. Appl., 16, 263 (1982).
V. P. Karassiov and A. B. Klimov, Phys. Lett. A, 189, 43 (1994).
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Paper submitted by the authors in English on 30 May 2006.
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Klimov, A.B., Sainz, I. Effective resonance transitions in quantum optical systems: Kinematic and dynamic resonances. J Russ Laser Res 27, 341–359 (2006). https://doi.org/10.1007/s10946-006-0018-8
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DOI: https://doi.org/10.1007/s10946-006-0018-8