Simultaneous approximate tracking of density matrices for a system of Schroedinger equations

TL;DR

This paper demonstrates that a system of multiple bilinear Schrödinger equations can approximately track any desired trajectories of density matrices using finite-dimensional control techniques, applicable to both bounded and unbounded operators.

Contribution

It introduces a method for approximate tracking of density matrices in multi-Schrödinger systems using Lie group control techniques, extending previous results to more general operators.

Findings

System can approximately track density matrix trajectories

Method applies to both bounded and unbounded Schrödinger operators

Tracking of phase and modulus simultaneously is generally impossible

Abstract

We consider a non-resonant system of finitely many bilinear Schroedinger equations with discrete spectrum driven by the same scalar control. We prove that this system can approximately track any given system of trajectories of density matrices, up to the phase of the coordinates. The result is valid both for bounded and unbounded Schroedinger operators. The method used relies on finite-dimensional control techniques applied to Lie groups. We provide also an example showing that no approximate tracking of both modulus and phase is possible