Engineering Dissipative Quasicrystals

TL;DR

This paper presents a method to engineer dissipative quasicrystals in open quantum systems, revealing how non-Hermitian physics influences their long-term dynamics and phase transitions.

Contribution

It introduces a systematic approach to create dissipative quasicrystals using non-Hermitian models and maps their eigenspectrum to the Liouvillian spectrum in quadratic fermionic systems.

Findings

Short-time dynamics governed by non-Hermitian Aubry-Andre-Harper model

Long-time steady states exhibit unique phase transitions

Exact spectral mapping enables engineered quantum dynamics

Abstract

We discuss the systematic engineering of quasicrystals in open quantum systems where quasiperiodicity is introduced through purely dissipative processes. While the resulting short-time dynamics is governed by non-Hermitian variants of the Aubry-Andre-Harper model, we demonstrate how phases and phase transitions pertaining to the non-Hermitian quasicrystals fundamentally change the long-time, steady-state-approaching dynamics under the Lindblad master equation. Our schemes are based on an exact mapping between the eigenspectrum of the Liouvillian superoperator with that of the non-Hermitian Hamiltonian, under the condition of quadratic fermionic systems subject to linear dissipation. Our work suggests a systematic route toward engineering exotic quantum dynamics in open systems, based on insights of non-Hermitian physics.