Synthesis of stabilizing switched controllers for N-dimensional quantum angular momentum systems

TL;DR

This paper develops a class of feedback controllers that ensure global stability of finite-dimensional quantum angular momentum systems by employing a parameterized switching control law, guaranteeing stability around a chosen eigenstate.

Contribution

It introduces a new class of stabilizing switched controllers parameterized by a switching parameter, extending previous control laws to N-dimensional quantum systems.

Findings

Stability is guaranteed for switching parameters between 0 and 1/N.

The control law is based on the Mirrahimi & van Handel approach.

The controllers stabilize the system around a specific eigenstate.

Abstract

This paper provides a class of feedback controllers that guarantee global stability of quantum angular momentum systems. The systems are in general finite dimensions and the stability is around an assigned eigenstate of observables with a specific form. It is realized by employing the control law which was proposed by Mirrahimi & van Handel. The class of stabilizing controllers is parameterized by a switching parameter and we show that the parameter between 0 and 1/N assures the stability, where N is the dimension of the quantum systems.