Lie transformation on shortcut to adiabaticity in parametric driving quantum system

TL;DR

This paper introduces a unified Lie algebraic framework that connects different shortcut to adiabaticity techniques, simplifying the design of rapid quantum state transformations without needing instantaneous states or invariants.

Contribution

It presents a consistent method that unifies counterdiabatic and invariant-based approaches using Lie algebra, streamlining the development of STA schemes for various potentials.

Findings

Unified Lie algebraic framework for STA techniques

Simplified design of STA without requiring instantaneous states

General STA schemes applicable to different potentials

Abstract

Shortcut to adiabaticity (STA) is a speed way to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxiliary counterdiabatic fields or finding new Hamiltonians that own dynamical invariants to constraint the system into the adiabatic paths. In this paper, a consistent method is introduced to naturally connect the above two techniques with a unified Lie algebraic framework, which neatly removes the requirements of finding instantaneous states in the transitionless driving method and the invariant quantities in the invariant-based inverse engineering approach. The general STA schemes for different potential expansions are concisely achieved with the aid of this method.