Time-rescaling of Dirac dynamics: shortcuts to adiabaticity in ion traps and Weyl semimetals

TL;DR

This paper explores how time-rescaling can be used to achieve adiabatic-like dynamics in Dirac systems, specifically in ion traps and Weyl semimetals, by transforming the Hamiltonian into effective potentials.

Contribution

It demonstrates a method to apply time-rescaling to Dirac dynamics, enabling adiabatic control without relying on eigenspectrum knowledge.

Findings

Time-rescaling effectively absorbs time dependence into potentials.

Application to ion traps shows improved adiabatic control.

Creation of Weyl points can be achieved adiabatically using this method.

Abstract

Only very recently, rescaling time has been recognized as a way to achieve adiabatic dynamics in fast processes. The advantage of time-rescaling over other shortcuts to adiabaticity is that it does not depend on the eigenspectrum and eigenstates of the Hamiltonian. However, time-rescaling requires that the original dynamics are adiabatic, and in the rescaled time frame the Hamiltonian exhibits non-trivial time-dependence. In this work, we show how time-rescaling can be applied to Dirac dynamics, and we show that all time-dependence can be absorbed into the effective potentials through a judiciously chosen unitary transformation. This is demonstrated for two experimentally relevant scenarios, namely for ion traps and adiabatic creation of Weyl points.