Controllability of spin-boson systems

Abstract : In this paper we study the so-called spin-boson system, namely {a two-level system} in interaction with a distinguished mode of a quantized bosonic field. We give a brief description of the controlled Rabi and Jaynes--Cummings models and we discuss their appearance in the mathematics and physics literature. We then study the controllability of the Rabi model when the control is an external field acting on the bosonic part. Applying geometric control techniques to the Galerkin approximation and using perturbation theory to guarantee non-resonance of the spectrum of the drift operator, we prove approximate controllability of the system, for almost every value of the interaction parameter.
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Journal of Mathematical Physics, American Institute of Physics (AIP), 2015, 56
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Soumis le : mercredi 18 mars 2015 - 10:46:51
Dernière modification le : mardi 23 octobre 2018 - 11:00:02
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  • HAL Id : hal-01132741, version 1
  • ARXIV : 1503.05937


Ugo Boscain, Paolo Mason, Gianluca Panati, Mario Sigalotti. Controllability of spin-boson systems. Journal of Mathematical Physics, American Institute of Physics (AIP), 2015, 56. 〈hal-01132741〉



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