Control of a two level open quantum system

Author

D´Alessandro, Domenico ; Dobrovitski, Viatches

Author_Institution

Dept. of Math., Iowa State Univ., Ames, IA, USA

Volume

1

fYear

2002

fDate

10-13 Dec. 2002

Firstpage

40

Abstract

We study the control problem for a general (finite dimensional) quantum system interacting with a bath. In the Hamiltonian formulation, the overall (system+environment) system varies on a Hilbert space which is the tensor product of the system and environment Hilbert spaces. We use sensitivity functions as a tool to compare the control laws and trajectories in this formulation. We treat the example of a spin 1/2 particle in a spin bath in detail. For this system, using optimal control theory and first order sensitivity as the cost, we explicitly derive the minimum decoherence controls.

Keywords

Hilbert spaces; Lie algebras; dynamics; optimal control; quantum theory; sensitivity analysis; Hamiltonian formulation; Hilbert space; Lie algebra; dynamics; minimum decoherence controls; optimal control; sensitivity functions; spin bath; spin particle; tensor product; two level open quantum system; Control systems; Controllability; Helium; Hilbert space; Magnetic field measurement; Mathematics; Mechanical systems; Open loop systems; Optimal control; Quantum mechanics;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2002, Proceedings of the 41st IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-7516-5

Type

conf

DOI

10.1109/CDC.2002.1184464

Filename

1184464