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Analysis and Mathematical Physics pp 211–232Cite as

Application of ATS in a Quantum-optical Model

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Part of the book series: Trends in Mathematics ((TM))

Abstract

The problem of the interaction of a single two-level atom with a single mode of the quantized electromagnetic field in a coherent state in an ideal resonator in the resonance case is considered. The evolution in time of the atomic inversion, represented by the Jaynes-Cummings sum, is studied. On the basis of the application of the theorem on the approximation of a trigonometric sum by a shorter one (ATS), a new efficient method for approximating the Jaynes-Cummings sum is constructed. New asymptotic formulas for the atomic inversion are found, which approximate it on various time intervals, defined by relation between the atom-field coupling constant and the average photon number in the resonator field before the interaction of the field with the atom. The asymptotics that we obtain give the possibility to predetermine the details of the process of the inversion in the Jaynes-Cummings model depending on the field characteristics.

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Author information

Authors and Affiliations

  1. Steklov Institute of Mathematics of RAS, Gubkina str., 8, Moscow, 119991, Russia

    Anatolii A. Karatsuba

  2. Dorodnicyn Computing Center of RAS, Vavilova str., 40, Moscow, 119333, Russia

    Ekatherina A. Karatsuba

Authors
  1. Anatolii A. Karatsuba
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  2. Ekatherina A. Karatsuba
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology (KTH), 100 44, Stockholm, Sweden

    Björn Gustafsson

  2. Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008, Bergen, Norway

    Alexander Vasil’ev

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Karatsuba, A.A., Karatsuba, E.A. (2009). Application of ATS in a Quantum-optical Model. In: Gustafsson, B., Vasil’ev, A. (eds) Analysis and Mathematical Physics. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9906-1_13

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