Abstract
The stochastic and quantum dynamics of open quantum systems interacting with stochastic perturbations in considered. The master equations for one time and multi-time correlation functions of such a system are derived to all orders in the interaction with the stochastic perturbations. The importance of the non-markovian character of such equations in the study of various problems in optical resonance is discussed. The simplified form of the non-markovian master equations in Born approximation is also given. It is shown that such non-markovian master equations in Born approximation are exact if there is only one random perturbation, of the telegraphic signal type, acting on the system. The master equations for the linear response functions of an open system interacting with stochastic perturbations are also derived. The non-markovian master equations for multitime correlations are used to study the behaviour of two level atoms interacting with fluctuating laser fields. Both amplitude and phase fluctuations are taken into account. Explicit results are presented for the spectrum of resonance fluorescence, absorption spectrum, photon antibunching effects etc. The calculations are done for arbitrary values of the relaxation parameters and intial conditions. In general the fluorescence spectrum is found to be asymmetric for off resonant fields.
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Agarwal, G.S.: (a) Phys. Rev. Letters37, 1383 (1976); (b) Phys. Rev.A 18, 1490 (1978)
Eberly, J.H.: Phys. Rev. Letters37, 1387 (1976)
Kimble, H.J., Mandel, L.: Phys. Rev. A15, 689 (1977) Avan, P., Cohen Tannoudji, C.: J. Phys. B10, 155 (1977) Zoller, P.: J. Phys. B10, L321 (1977)
Mollow, B.R.: Phys. Rev.188, 1969 (1969); A12, 1919 (1975); A13, 758 (1976) Wu, F., Grove, R.F., Ezekiel, S.: Phys. Rev. Lett.34, 1485 (1975) Walther, H.: Proc. Second Laser Spectroscopy Conference Haroche, S. et. al. (ed.) Berlin-Heidelberg-New York: Springer 1975 p. 358 Schuda, F., Stroud, C.R., Hercher, M.: J. Phys. B 7, L 198 (1974) Agarwal, G.S., Brown, A.C., Narducci, L.M., Vetri, G.: Phys. Rev. A15, 1613 (1977) Kimble, H., Mandel, L.: Phys. Rev. A13, 2123 (1976) Walls, D., Carmichael, H.J.: J. Phys. B8, L 77 (1975) Cohen Tannoudji, C.: Frontiers in Laser Spectroscopy Balian, R., Haroche, S., Liberman, S. (eds.) Amsterdam: North Holland 1976
Agarwal, G.S.: Springer Tracts in Modern Physics Vol. 70 Sect. 18. Höhler, G. et al. (eds.) Berlin-Heidelberg-New York: Springer 1974
Takagahara, T., Hanamura, E., Kubo, R.: J. Phys. Soc. (Japan)43, 802 (1977);43, 811 (1977)
Mollow, B.R.: Phys. Rev. A5, 2217 (1972)
Carmichael, H.J., Walls, D.: J. Phys. B9, 1199 (1976); Kimble, H., Mandel, L.: Phys. Rev. A13, 2123 (1976)
Agarwal, G.S.: Phys. Rev. A15, 814 (1977)
Zwanzig, R.W. In: Lectures in Theoretical Physics Brittin, W.E. et al. (eds.) P. 106 New York: Gordon and Breach 1961; Physica30, 1109 (1964)
Agarwal, G.S.: Progress in Optics Wolf, E. (ed.) Vol. XI, P.1. Amsterdam: North Holland 1973
Haake, F.: Springer Tracts in Modern Physics Höhler, G., et al. (ed.) Vol. 66, P.98. Berlin-Heidelberg-New York: Springer 1973
Bourret, R.C.: Nuovo Cim.26, 1 (1962); Can. J. Phys.40, 782 (1962); ibid43, 619 (1965); ibid44, 2519 (1966)
Martin, P.C. In: Many Body Physics, Dewitt, C., Belian (eds.) P.37. New York: Gordon and Breach 1968
Rhodes, W.: Chem. Phys.22, 95 (1977) and the references therein
Haroche, S. In: Laser Spectroscopy of Atoms and Molecules Walther, H. (ed.) P.253. Berlin-Heidelberg-New York: Springer 1976
Allen, L., Eberly, J.H.: Optical Resonance and Two Level Atom, New York: Wiley, Interscience 1975; Brewer, R. In: Non-Linear Spectroscopy Bloembergen, N. (ed.) P. 87. Amsterdam: North-Holland 1977
Wolf, E.: Proc. Roy. Soc. (London)230, 246 (1955) Beran, M.J., Parrent, G.B.: Theory of Partial Coherence, Englewood Cliffs, NJ: Prentice-Hall 1964 Beran, M.J.: Statistical Continuum Theories, New York: Interscience 1968
Haken, H., Reinekar, P.: Z. Physik249, 253 (1972) Haken, H., Strobl, G.: Z. Physik262, 135 (1973)
Morrison, J.A.: J. Math. Phys.11, 3200 (1970) and references therein Adomin, G.: J. Math. Phys.11, 1069 (1970);12, 1944 (1971);12, 1948 (1971); Tatarski, V.I.: Zh. Eksperim. i. Teor Fiz42, 1386 (1962);46, 1399 (1964)
Frisch, U. In: Probabilistic Methods in Applied Mathematics Bharucha, A.T. Reid, (ed.) Vol. I, P. 75. New York: Academic Press 1968
Blume, M., Tjon, J.A.: Phys. Rev.165, 446 (1968); Clauser, M.J., Blume, M.: Phys. Rev. B3, 583 (1977)
Kubo, R. In: Stochastic Processes in Chemical Physics Shuler, K.E. (ed.) P. 101 New York: Interscience 1969
Graham, R.: Z. Physik210, 319 (1968) Dixit, S.N., Lambropoulos, P.: Phys. Rev. Letters40, 111 (1978)
Lax, M.: Phys. Rev.172, 350 (1968); Haken, H., Weidlich, W.: Z. Physik205, 96 (1967)
Kubo, R.: J. Math. Phys.4 (1963); Fox, J.: J. Math. Phys.13, 1196 (1972)
Redfield, A.G.: IBM J. Res. Develop1, 19 (1957) Abragam, A.: Principles of Nuclear Magnetism Oxford: Clarendon Press 1961
Arygres, P.N. In: Lectures in Theoretical Physics, Brittin, W.E. (ed.) Vol. VIIIA, P. 753 Boulder: University of Colorado Press; see also Kenke, V.M.: Phys. Rev. A7, 772 (1973)
Kimble, H.J., Degenais, M., Mandel, L.: Phys. Rev. Lett.39, 691 (1977)
Wu, F.Y., Ezekiel, S., Ducloy, M., Mollow, B.R.: Phys. Rev. Lett.38, 1077 (1977)
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Agarwal, G.S. Master equations for time correlation functions of a quantum system interacting with stochastic perturbations and applications to emission and absorption line shapes. Z Physik B 33, 111–124 (1979). https://doi.org/10.1007/BF01325819
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DOI: https://doi.org/10.1007/BF01325819