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Quantum averaging and resonances: two-level atom in a one-mode quantized field

M. Amniat-Talab·S. Guerin·H. R. Jauslin
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Abstract

We construct a non-perturbative approach based on quantum averaging combined with resonant transformations to detect the resonances of a given Hamiltonian and to treat them. This approach, that generalizes the rotating-wave approximation, takes into account the resonances at low field and also at high field (non-linear resonances). This allows to derive effective Hamiltonians that contain the qualitative features of the spectrum, i.e. crossings and avoided crossings, as a function of the coupling constant. At a second stage the precision of the spectrum can be improved quantitatively by standard perturbative methods like contact transformations. We illustrate this method to determine the spectrum of a two-level atom interacting with a single mode of a quantized field.

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M. Amniat-Talab, S. Guerin, H. R. Jauslin. 2003-12-09. Quantum averaging and resonances: two-level atom in a one-mode quantized field. https://arxiv.org/abs/quant-ph/0312077

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