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Jaynes-Cummings model and quantum chaos

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     * [5]Prof. Marek Kus, Center for Theoretical Physics PAS, Warsaw

   Prof. Marek Kus accepted the invitation on 7 July 2011

   Jaynes-Cummings model and [6]quantum chaos refers to an important model of
   quantum optics in a regime of quantum chaos

   Short note and Related References added by [7]Scholarpedia Editor D.Shepelyansky
   in May 2020

   The Jaynes-Cummings model [1] is the cornerstone system of quantum optics
   describing interactions of resonator photons with an atom, considered in a
   two-level approximation. The usual experimental conditions correspond to a weak
   coupling constant between photons and atom. In this regime the quantum evolution
   of the system is integrable demonstrating revival energy exchange between photons
   and atom [1,2,3,4]. Such revival behavior had been first observed in experiments
   with Rydberg atoms inside a superconducting cavity [5].

   At strong coupling the [8]dynamics may become nontrivial with the emergence of
   classical chaos when the dynamics of [9]oscillator is treated as classical and
   two-level atom as quantum [6] (see also [7]). However, for one atom even with a
   strong coupling to a quantum photonic field the evolution, spectrum and
   eigenstates are still rather simple due to a total energy balance [8],[9]. The
   regime of quantum chaos with the level spacing statisitcs of [10]Random Matrix
   Theory appears only when several two-level atoms are interacting with the
   quantized photonic field of resonator as it was shown in [10].

Related References

    1. E.T.Jaynes, F.W.Cummings, "Comparison of quantum and semiclassical radiation
       theories with application to the beam maser", Proc. IEEE. 51(1): 89 (1963)
    2. J.J.Sanchez-Mondragon, N.B.Narozhny, J.H.Eberly, "Theory of
       spontaneous-emission line shape in an ideal cavity", Phys. Rev. Lett. 51: 550
       (1983)
    3. L.Allen, J.H.Eberly, "Optical [11]resonance and two-level atoms", Dover
       Publs. Inc., New York (1987)
    4. M.O.Scully, M.S.Zubairy, "Quantum optics", Cambridge University Press,
       Cambridge, England, (1997)
    5. G.Rempe, H.Walther, N.Klein, "Observation of quantum collapse and revival in
       a one-atom maser", Phys. Rev. Lett. 58(4): 353 (1987)
    6. P.I.Belobrov, G.M.Zaslavskii, G.Kh.Tartakovskii, "Stochastic breaking of
       bound states in a system of atoms interacting with a radiation field", Sov.
       Phys. JETP 44(5): 945 (1976)
    7. J.R.Ackerhalt, P.W.Milonni, M.-L.Shin, "Chaos in quantum optics", Physics
       Reports 128(4-5): 205 (1985)
    8. R.Graham, M.Hohnerbach, "Two-state system coupled to a boson mode: Quantum
       dynamics and classical approximations", Z. Phys. B Cond. Mat. 57: 233 (1984)
    9. M.Kus, "Statistical properties of the spectrum of the two-level system",
       Phys. Rev. Lett. 54: 1343 (1985)
   10. R.Graham, M.Hohnerbach, "Statistical spectral and dynamical properties of
       two-level systems", Phys. Rev. Lett. 57: 1378-1378 (1986)

See also internal links

   [12]Random matrix theory, [13]Bohigas-Giannoni-Schmit conjecture
   Sponsored by: [14]Dima Shepelyansky, Laboratoire de Physique Théorique, CNRS,
   Université Paul Sabatier, Toulouse
   Retrieved from
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   and_quantum_chaos&oldid=193531"
   [16]Category:
     * [17]Quantum Chaos

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