Shortcuts to adiabaticity using flow fields

TL;DR

This paper introduces a unified framework using flow fields to construct shortcuts to adiabaticity across quantum, classical, and stochastic systems, providing compact formulas and analyzing singularities.

Contribution

It develops a general flow field-based method for creating shortcuts to adiabaticity applicable to various dynamics, unifying previous approaches and offering new insights.

Findings

Compact expressions for counterdiabatic Hamiltonians and fast-forward potentials.

Numerical simulations demonstrating the effectiveness of the method.

A criterion for predicting singularities in quantum shortcuts.

Abstract

A $\textit{shortcut to adiabaticity}$ is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a $\textit{counterdiabatic}$ Hamiltonian that causes a system to follow the adiabatic evolution at all times, or it might utilize a $\textit{fast-forward}$ potential, which returns the system to the adiabatic path at the end of the process. We develop a general framework for constructing shortcuts to adiabaticity from $\textit{flow fields}$ that describe the desired adiabatic evolution. Our approach encompasses quantum, classical and stochastic dynamics, and provides surprisingly compact expressions for both counterdiabatic Hamiltonians and fast-forward potentials. We illustrate our method with numerical simulations of a model system, and we compare our shortcuts with previously obtained results. We also consider the semiclassical connections between our quantum and classical shortcuts. Our method, like the fast-forward approach developed by previous authors, is susceptible to singularities when applied to excited states of quantum systems; we propose a simple, intuitive criterion for determining whether these singularities will arise, for a given excited state.