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Quantum Theory of Resonant Oscillation

Shigemi Araki

Published Oct 1, 1981• 0 citations
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Quantum Theory of Resonant Oscillation

Shigemi Araki

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Abstract The paper shows mechanisms of both the pumping and energy decay of an ‘isolated’ oscillator. The oscillator is only coupled non-resonantly with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the ‘isolated’ oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian. The original model is reduced to two ‘independent’ open systems, with each containing original oscillators connected with their effective independent thermal baths, whose parameters are determined. The paper also gives a description of the obtained model in terms of quantum stochastic differential equations.

Physica Scripta•Jan 22, 2020•18 citations
The speci c features of the theory of resonant interactions of electromagnetic coherent elds with an anharmonic oscillator, as compared to the case of a multilevel atom, are highlighted. It is shown that within the framework of the local approach - the algebraic resonance perturbation theory - it is possible to account for the requirements of the global approach of the theory of open quantum systems. Based on the auxiliary model of the «internal nonlinearity» of the anharmonic oscillator, the possible conditions for the resonance of a coherent wave with an anharmonic oscillator involving the absorption of a single photon are analyzed.
Abstract The specific features of the theory of resonant interactions of electromagnetic coherent fields with an anharmonic oscillator, as compared to the case of a multilevel atom, are highlighted. It is shown that within the framework of the local approach—the algebraic resonance perturbation theory—it is possible to account for the requirements of the global approach of the theory of open quantum systems. Based on the auxiliary model of the ‘‘internal nonlinearity’’ of the anharmonic oscillator, the possible conditions for the resonance of a coherent wave with an anharmonic oscillator involving the absorption of a single photon are analyzed.
Abstract The paper shows mechanisms of both the pumping and energy decay of an ‘isolated’ oscillator. The oscillator is only coupled non-resonantly with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the ‘isolated’ oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian. The original model is reduced to two ‘independent’ open systems, with each containing original oscillators connected with their effective independent thermal baths, whose parameters are determined. The paper also gives a description of the obtained model in terms of quantum stochastic differential equations.