Controllability of Quantum Systems on the Lie Group SU(1,1)

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

This paper examines the controllability for quantum control systems with SU(1,1) dynamical symmetry, namely, the ability to use some electromagnetic field to redirect the quantum system toward a desired evolution. The problem is formalized as the control of a right invariant bilinear system evolving on the Lie group SU(1,1) of two dimensional special pseudo-unitary matrices. It is proved that the elliptic condition of the total Hamiltonian is both sufficient and necessary for the controllability. Conditions are also given for small time local controllability and strong controllability. The results obtained are also valid for the control systems on the Lie groups SO(2,1) and SL(2,R).

Keywords

Optimization and Control, Quantum Algebra

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/136583

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.3147
 http://arxiv.org/abs/0708.3147

Collections

arXiv