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Progress in mathematical physics

Chaos in Microwave Resonators

H.‐J. Stöckmann

Published Jan 1, 2013• 8 citations
Publisher
DOI
10.1007/978-3-0348-0697-8_5

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The semiclassical and quantum dynamics of two ultrastrongly coupled nonlinear resonators cannot be explained using the discrete nonlinear Schrödinger equation or the Bose-Hubbard model, respectively. Instead, a model beyond the rotating wave approximation must be studied. In the semiclassical limit this model is not integrable and becomes chaotic for a finite window of parameters. For the quantum dimer we find corresponding regions of stability and chaos. The more striking consequence for both semiclassical and quantum chaos is that the tunneling time between the sites becomes unpredictable. These results, including the transition to chaos, can be tested in experiments with superconducting microwave resonators.
t is proved analytically and numerically that, under certain conditions, the reversible spontaneous emission of two-level atoms moving in a high- Q resonator and described quantum-classically can be chaotic in the sense of the exponential sensitivity with respect to the initial conditions. The wavelet analysis of the vacuum Rabi oscillations showed that this chaos is structural. The numerical estimates showed that a Rydberg atom maser with a superconducting microwave resonator operating in a strong coupling mode is a promising device for detecting mani-festations of the dynamic chaos in the reversible spontaneous emission.