Energy Optimal Control for Quantum System Evolving on SU(1,1)

TL;DR

This paper derives energy optimal control strategies for quantum systems with SU(1,1) symmetry, providing explicit solutions using Lie group maximum principle, including elliptic function controls and constant abnormal controls.

Contribution

It analytically characterizes all optimal controls for SU(1,1) quantum systems, including normal and abnormal extremals, using Lie group maximum principle.

Findings

Normal extremal controls expressed by Weierstrass elliptic functions

Abnormal extremal controls are constant functions of time

Complete set of optimal controls analytically obtained

Abstract

This paper discusses the energy optimal control problem for the class of quantum systems that possess dynamical symmetry of SU(1,1), which are widely studied in various physical problems in the quantum theory. Based on the maximum principle on Lie group, the complete set of optimal controls are analytically obtained, including both normal and abnormal extremals. The results indicate that the normal extremal controls can be expressed by the Weierstrass elliptic function, while the abnormal extremal controls can only be constant functions of time t.