Abstract
We consider a model of atomic radiators in a dielectric medium and its optical characteristics. In the framework of the microscopic approach and the Bogolyubov-Born-Green-Kirkwood-Yvon method, we obtain a chain of coupled equations for reduced density matrices and correlation operators of atomic particles and modes of a quantized field. We derive a closed system of equations describing the evolution of radiators in the model medium under the action of external radiation. We calculate the effective spontaneous relaxation rate in the presence of the local field produced by the medium. For the first time, we demonstrate the relation between micro and macro approaches to the solution of the problem involving a change in the spontaneous radiation rate in the medium.
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References
R. J. Glauber and M. Lewenstein, Phys. Rev. A, 43, 467–491 (1991).
P. W. Milonni, J. Mod. Opt., 42, 1991–2004 (1995).
G. Nienhuis and C. Th. J. Alkemade, Phys. B+C, 81, 181–188 (1976).
M. E. Crenshaw and C. M. Bowden, Phys. Rev. Lett., 85, 1851–1854 (2000); arXiv:quant-ph/0004101v1 (2000).
M. E. Crenshaw and C. M. Bowden, Phys. Rev. A., 63, 013801 (2000).
M. E. Crenshaw, Phys. Rev. A, 78, 053827 (2008); arXiv:0805.2134v3 [quant-ph] (2008).
S. Scheel, L. Knoll, and D.-G. Welsch, Phys. Rev. A, 60, 4094–4104 (1999); arXiv:quant-ph/9904015v1 (1999).
M. Born and E. Wolf, Principles of Optics, Pergamon, Oxford (1969).
F. J. P. Schuurmans, D. T. N. de Lang, G. H. Wegdam, R. Sprik, and A. Lagendijk, Phys. Rev. Lett., 80, 5077–5080 (1998).
A. A. Panteleev, Vl. K. Roerich, and A. N. Starostin, JETP, 96, 222–240 (2003).
M. Bonitz, Quantum Kinetic Theory, B. G. Teubner, Stuttgart (1998).
Yu. L. Klimontovich, Statistical Physics [in Russian], Nauka, Moscow (1982); English transl., Harwood, New York (1986).
Yu. L. Klimontovich, The Kinetic Theory of Electromagnetic Processes [in Russian], Nauka, Moscow (1980); English transl., Springer, Berlin (1983).
M. G. Gladush, A. A. Panteleev, and Vl. C. Roerich, JETP, 103, 206–217 (2006).
A. Kuditcher, M. P. Hehlen, C. M. Florea, K. W. Winick, and S. C. Rand, Phys. Rev. Lett., 84, 1898–1901 (2000).
É. G. Pestov, Trudy Fiz. Inst. Lebedev., 187, 60–116 (1988).
M. G. Gladush, D. V. Kuznetsov, A. A. Panteleev, and Vl. K. Roerich, “Emission spectra and intrinsic optical bistability in a two-level medium,” arXiv:1010.29691 [quant-ph] (2010).
A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics [in Russian], Nauka, Moscow (1981); English transl. prev. ed., Consultants Bureau, New York (1957).
Vl. K. Roerich, A. N. Starostin, and A. A. Panteleev, “Many-body approaches to time-dependent resonance fluorescence,” in: Progress in Nonequilibrium Green’s Functions II (M. Bonitz and D. Semkat, eds.), World Scientific, Singapore (2003), pp. 103–111.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 168, No. 2, pp. 261–280, August, 2011.
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Kuznetsov, D.V., Roerich, V.K. & Gladush, M.G. Using BBGKY hierarchies to study the effect of the local field on the rate of radiative relaxation of quantum systems in a dielectric medium. Theor Math Phys 168, 1078–1095 (2011). https://doi.org/10.1007/s11232-011-0089-8
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DOI: https://doi.org/10.1007/s11232-011-0089-8