Effective and efficient resonant transitions in periodically modulated quantum systems

• URL: http://arxiv.org/abs/2108.04360v1
• Date: Mon, 9 Aug 2021 20:59:56 GMT
• Title: Effective and efficient resonant transitions in periodically modulated quantum systems
• Authors: Isabel Sainz, Andr\'es Garc\'ia and Andrei B. Klimov
• Abstract summary: We analyse periodically modulated quantum systems with $SU(2)$ and $SU (1,1)$ symmetries. For coupled quantum systems we determine the efficient resonant transitions appearing as a result of time modulation and intrinsic non-linearities.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We analyse periodically modulated quantum systems with $SU(2)$ and $SU(1,1)$ symmetries. Transforming the Hamiltonian into the Floquet representation we apply the Lie transformation method, which allows us to classify all effective resonant transitions emerging in time-dependent systems. In the case of a single periodically perturbed system, we propose an explicit iterative procedure for the determination of the effective interaction constants corresponding to every resonance both for weak and strong modulation. For coupled quantum systems we determine the efficient resonant transitions appearing as a result of time modulation and intrinsic non-linearities.

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