Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems

We analyze 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...

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Bibliographic Details
Published in:Quantum reports 2021-03, Vol.3 (1), p.173-195
Main Authors: Sainz, Isabel, García, Andrés, Klimov, Andrei B.
Format: Article
Language:English
Subjects:
Algebra
Approximation
Modulation
periodic modulation
resonant interactions
System effectiveness
Time dependence
time dependent hamiltonians
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Summary:We analyze 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.
ISSN:2624-960X
2624-960X
DOI:10.3390/quantum3010011