Computational Mathematics and Modeling

, Volume 30, Issue 1, pp 68–79 | Cite as

Analytical Solution of the Quantum Master Equation for the Jaynes–Cummings Model

  • N. B. ViktorovaEmail author
  • Yu. I. Ozhigov
  • N. A. Skovoroda
  • K. N. Skurat

The article considers the dynamics of resonator photon occupancy (the probability of finding a photon in the resonator), atom excitation, and sink photon occupancy when a single photon escapes into the sink from an optical resonator populated by an atom in the ground and excited states. The photon-occupancy dynamics of the cavity is investigated using the Lindblad equation.


Lindblad equation Jaynes–Cummings model density matrix 


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  1. 1.
    N. B. Viktorova, Yu. I. Ozhigov, and N. A. Skovoroda, “Non-Rabi quantum revivals in the Jaynes–Cumming model,” Teoreticheskaya i Matematicheskaya Fizika, 189, No. 2, 312–320 (2016).MathSciNetCrossRefGoogle Scholar
  2. 2.
    E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE, 51, No. 1, 89–109 (1963).CrossRefGoogle Scholar
  3. 3.
    Yu. I. Ozhigov and N. A. Skovoroda, “Atomic excitation conductivity in a system of optical cavities,” Matem. Modelirovanie, 29, No. 12, 123–134 (2017).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • N. B. Viktorova
    • 1
    Email author
  • Yu. I. Ozhigov
    • 2
  • N. A. Skovoroda
    • 2
  • K. N. Skurat
    • 3
  1. 1.Russian State University of Humanities and Institute of Information Sciences and Security Technologies, Department of Applied MathematicsMoscowRussia
  2. 2.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia
  3. 3.Faculty of Information Systems and Security, Russian State University of Humanities, Department of Applied MathematicsMoscowRussia

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