Topological Operations Around Exceptional Points via Shortcuts to Adiabaticity

TL;DR

This paper develops fast, robust control protocols using shortcuts to adiabaticity to perform topological operations around exceptional points in non-Hermitian systems, overcoming challenges posed by spectral singularities.

Contribution

It introduces a novel control strategy for non-Hermitian Hamiltonians that enables topological operations without requiring slow adiabatic evolution, addressing limitations of existing shortcuts.

Findings

The proposed method effectively performs topological operations in a two-mode non-Hermitian system.

Standard shortcuts like transitionless driving are unsuitable for non-Hermitian systems due to spectral singularities.

The strategy is robust against parameter uncertainties and avoids faulty control protocols.

Abstract

The existence of singularities in the spectrum of non-Hermitian Hamiltonians leads to a non-trivial spectral topology which can be exploited to generate topological operations. However, their implementation has remained elusive due to the difficulty of generating a true adiabatic evolution. Here, we develop fast, robust control protocols that generate a desired topological operation. Our strategy relies on shortcuts to adiabaticity, but is not a trivial extension. The presence of spectral singularities renders the strategy developed for Hermitian Hamiltonians impractical as it will lead to faulty control protocols. Moreover, due to the dynamics sensitivity to parameter uncertainties, not all shortcuts to adiabaticity can be used in a realistic setting. We illustrate our method in the context of a two-mode non-Hermitian Hamiltonian and discuss why in general celebrated shortcuts to adiabaticiy like transitionless driving and superadiabatic transitionless driving are not appropriate control protocols for non-Hermitian systems.