On the control of spin-boson systems

Journal Article · Tue Sep 15 00:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4929543· OSTI ID:22479595

Boscain, Ugo ^[1]; Mason, Paolo ^[2]; Panati, Gianluca ^[3]; Sigalotti, Mario ^[4]

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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)

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.

• OSTI ID: 22479595
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 9; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BOSONS
CONTROL
DATA
GEOMETRY
PERTURBATION THEORY
SPIN