Chemistry Reference
In-Depth Information
GEOMETRIC OPTIMAL CONTROL OF SIMPLE
QUANTUM SYSTEMS
DOMINIQUE SUGNY
Laboratorie Interdisciplinaire Carnot de Bourgogne (ICB), UMR 5209
CNRS-Universite de Bourgogne, F-21078 Dijon Cedex, France
CONTENTS
I.
Introduction
II.
The Pontryagin Maximum Principle
A.
The End-Point Mapping
B.
The Pontryagin Maximum Principle
1.
The General Formulation
2.
The Euler-Lagrange Principle
3.
The Time-Minimal Control Problem
C.
Geometric Aspects of the Optimal Control Theory
D.
Indirect and Continuation Methods
E.
Second-Order Optimality Conditions: The Concept of Conjugate Points
III.
Application to the Control of a Three-Level Quantum System
A.
Formulation of the Problem
B.
Optimal Control of a Three-Level Quantum System: The Grushin Model
C.
Optimal Control of a Three-Level Quantum System by Laser Fields and von Neumann
Measurements
IV.
Application to the Time-Optimal Control of Two-Level Dissipative Quantum Systems
A.
The Kossakowski-Lindblad Equation for
N
-Level Dissipative Quantum Systems
B.
Construction of the Model
C.
Geometric Analysis of Lindblad Equation
1.
Symmetry of Revolution
2.
Spherical Coordinates
3.
The Optimal Control Problem
