Approximate stabilization of a quantum particle in a 1D infinite square potential well

TL;DR

This paper demonstrates how to nearly stabilize a quantum particle in a 1D infinite potential well using explicit feedback control laws, advancing quantum control techniques.

Contribution

It introduces explicit feedback laws that achieve almost global approximate stabilization of eigenstates in a quantum system with boundary conditions.

Findings

Proves almost global stabilization of eigenstates

Develops explicit feedback control laws

Applicable to quantum systems with boundary conditions

Abstract

We consider a non relativistic charged particle in a 1-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) time depending electric field. It is represented by a complex probability amplitude solution of a Schrodinger equation on a 1-dimensional bounded domain, with Dirichlet boundary conditions. We prove the almost global approximate stabilization of the eigenstates by explicit feedback laws.