Finite-time stabilization of ladder multi-level quantum systems

TL;DR

This paper introduces a novel continuous non-smooth control method for finite-time stabilization of ladder multi-level quantum systems, using fractional-order control laws and Lyapunov stability theory, validated through numerical simulations.

Contribution

It presents a new fractional-order control strategy with a Lyapunov-based proof for finite-time stabilization of ladder quantum systems.

Findings

Proposed a universal fractional-order control law.

Proved existence and uniqueness of solutions under the control law.

Validated effectiveness through numerical simulations on a three-level atomic system.

Abstract

In this paper, a novel continuous non-smooth control strategy is proposed to achieve finite-time stabilization of ladder quantum systems. We first design a universal fractional-order control law for a ladder n-level quantum system using a distance-based Lyapunov function, and then apply the Filippov solution in the sense of differential inclusions and the LaSalle's invariance principle to prove the existence and uniqueness of the solution of the ladder system under the continuous non-smooth control law. Both asymptotic stability and finite-time stability for the ladder system is rigorously established by applying Lyapunov stability theory and finite-time stability criteria. We also derive an upper bound of the time required for convergence to an eigenstate of the intrinsic Hamiltonian. Numerical simulations on a rubidium ladder three-level atomic system validate the effectiveness of the proposed method.