Abstract
An ensemble of two-level radiators in a lossless cavity is considered as interacting with a resonant eigenmode field taking into account the feedback effect of the radiators on the field. In a semiclassical approximation, this dynamical system is described by the Maxwell-Bloch equations and is shown to have two control parameters, namely, the individual and cooperative Rabi frequencies. In the neoclassical Jaynes-Cummings treatment, a pure quantum-level description is converted to a set of closedc-number equations for quantum expectation values with a single control parameter (the cooperative vacuum Rabi frequency). We develop also a group-theoretical description for both of these models, which provides further insight into the general dynamic behavior. Increasing one of the model's control parameters, we investigate numerically the onset of dynamical chaos in field-atom interaction by calculating the maximum Lyapunov exponent of the Maxwell-Bloch and the Jaynes-Cummings dynamical systems. The onset is shown to differ depending on the model adopted, the control parameter used, and the initial conditions chosen. Possible candidates for experimentally observable (semi) quantum chaos in a system of dynamically driven two-level radiators are discussed by estimating the orders of magnitudes for the respective control parameters in actual quantum electrodynamical systems. It is shown that quantum-well excitons in fabricated semiconductor microcavities are likely candidates for experimental confirmation of transitions to dynamical chaos which have been revealed numerically in this study.
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Translated from a manuscript submitted December 25, 1995.
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Prants, S.V. Dynamical complexity of driven two-level systems. II. Dynamical driving by a self-consistent radiation field. J Russ Laser Res 18, 69–86 (1997). https://doi.org/10.1007/BF02558669
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DOI: https://doi.org/10.1007/BF02558669