Quantum Inf Process (2015) 14:2397–2418
Approximate controllability of the two trapped ions
· Mario Sigalotti
Received: 10 December 2014 / Accepted: 7 April 2015 / Published online: 21 April 2015
© Springer Science+Business Media New York 2015
Abstract We prove the approximate controllability of a bilinear Schrödinger equation
modelling a two trapped ions system. A new spectral decoupling technique is intro-
duced, which allows to analyze the controllability of the inﬁnite-dimensional system
through ﬁnite-dimensional considerations.
In this paper we study the controllability of a system modelling a two trapped ions
system driven by two laser beams.
1.1 The model
The two trapped ions system models a pair of identical charged particles conﬁned to
a small region of the space. Both ions are stabilized by the same spatial oscillation,
Esteban Paduro was supported in part by scholarship CONICYT Magíster Nacional 2012, Project
FONDECYT 1120610 and Project CONICYT ACT-1106.
Mario Sigalotti was partially supported by the European Research Council, ERC StG 2009 GeCoMethods,
Contract Number 239748, and by the iCODE institute, research project of the Idex Paris-Saclay.
Departamento de Matemática, Universidad Federico Santa María, Valparaíso, Chile
Team GECO, Centre de Recherche Saclay - Île-de-France, INRIA, Palaiseau, France