Parametric instability and Hamiltonian chaos in cavity semiclassical electrodynamics |
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Authors: | S V Prants L E Kon’kov |
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Institution: | (1) Pacific Oceanographic Institute, Far East Branch of the Russian Academy of Sciences, 690041 Vladivostok, Russia |
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Abstract: | We study the nonlinear dynamics of the interaction of two-level atoms and a selected mode of a high-Q cavity with frequency modulation analytically and numerically. In the absence of modulation, the corresponding semiclassical
Heisenberg equations for the expectation values of the collective atomic observables and the field-mode amplitudes allow,
in the rotating wave approximation and in the strong-coupling limit, an exact solution with arbitrary detuning. Using this
solution, we detect the coherent effect of trapping of the population of atomic levels and of trapping of the number of photons
in the cavity. The explanation for this effect lies in the destructive interference of the atomic dipoles and the field mode.
The integrable version of the system of equations exhibits a separatrix near which a stochastic layer is formed when modulation
is introduced. The width of the layer is found to gradually increase with degree of modulation, and finally it fills the entire
energy-permissible volume of the phase space. We show that the rotating wave approximation does not hinder the formation of
Hamiltonian chaos in cavity semiclassical electrodynamics. The calculation of the maximum Lyapunov indices of nonlinear (in
this approximation) equations of motion as functions of the modulation frequency δ and the frequency of natural Rabi oscillations of the atom-field system, Ω, suggests that Hamiltonian chaos appears first
in the area of the fundamental parametric resonance, δ/2Ω≃1. Parametric instability increases with increasing modulation and decreasing detuning from the atom-field resonance,
generating at exact resonance new areas of chaos corresponding to multiple parametric resonances. The results of numerical
experiments and estimates of the characteristic parameters show that Rydberg atoms placed in a high-Q microwave cavity are possible objects for observing parametric instability and dynamical chaos.
Zh. éksp. Teor. Fiz. 115, 740–753 (February 1999) |
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