Quantum control and quantum speed limits in supersymmetric potentials

TL;DR

This paper investigates how supersymmetry in quantum mechanics can be used to analyze and control the dynamics, shortcuts to adiabaticity, and quantum speed limits across different supersymmetric partner potentials, exemplified by the infinite box.

Contribution

It introduces a framework leveraging supersymmetry to study quantum control and speed limits across partner potentials, providing new insights into quantum dynamics.

Findings

Supersymmetry links the dynamics of different eigenstates.

The framework enables analysis of shortcuts to adiabaticity.

Quantum speed limits can be studied across supersymmetric partners.

Abstract

Supersymmetry allows one to build a hierarchy of Hamiltonians that share the same spectral properties and which are pairwise connected through common superpotentials. The iso-spectral properties of these Hamiltonians imply that the dynamics and therefore control of different eigenstates are connected through supersymmetric intertwining relations. In this work we explore how this enables one to study general dynamics, shortcuts to adiabaticity (STA) and quantum speed limits for distinct states of different supersymmetric partner potentials by using the infinite box as an example.