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Title: On the control of spin-boson systems

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.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Centre National de Recherche Scientifique (CNRS), CMAP, École Polytechnique and Team GECO, INRIA-Centre de Recherche Saclay, Route de Saclay, 91128 Palaiseau Cedex (France)
  2. CNRS-L2S-CentraleSupelec, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette (France)
  3. Dipartimento di Matematica, “La Sapienza” Università di Roma, Piazzale Aldo Moro 2, 00185 Rome (Italy)
  4. Team GECO, INRIA-Centre de Recherche Saclay and CMAP, École Polytechnique, Route de Saclay, 91128 Palaiseau Cedex (France)
Publication Date:
OSTI Identifier:
22479595
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 9; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BOSONS; CONTROL; DATA; GEOMETRY; PERTURBATION THEORY; SPIN