Title :
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
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;
Conference_Titel :
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
Print_ISBN :
0-7803-7516-5
DOI :
10.1109/CDC.2002.1184464
