Engineering Dissipative Quasicrystals

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.

arXiv comment9 pages, 4 figures

References in corpus (47)

• Edge states and topological invariants of non-Hermitian systems
• Many-body localization, thermalization, and entanglement
• Anderson localization of a non-interacting Bose-Einstein condensate
• Non-Hermitian Physics
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Topological phases of non-Hermitian systems
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological States and Adiabatic Pumping in Quasicrystals
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Non-Hermitian Chern bands
• Non-Hermitian Boundary Modes
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Topology by Dissipation in Atomic Quantum Wires
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Critical non-Hermitian Skin Effect
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Topological phase transition in non-Hermitian quasicrystals
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Observation of the topological Anderson insulator in disordered atomic wires
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• Edge states and topological phases in one-dimensional optical superlattices
• Algebraic versus exponential decoherence in dissipative many-particle systems
• Simulation methods for open quantum many-body systems
• Quantum critical behavior at the many-body-localization transition
• Tenfold Way for Quadratic Lindbladians
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Critical and bicritical properties of Harper's equation with next nearest neighbor coupling
• Anderson localization in the Non-Hermitian Aubry-André-Harper model with physical gain and loss
• Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model
• Many-body critical phase: extended and nonthermal
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• PT Symmetric Aubry-Andre Model
• Observation of topological phase with critical localization in a quasi-periodic lattice
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• PT-restoration via increased loss-gain in PT-symmetric Aubry-Andre model
• Localization, $\mathcal{P}\mathcal{T}$-Symmetry Breaking and Topological Transitions in non-Hermitian Quasicrystals
• Damping transition in an open generalized Aubry-André-Harper model
• PT-symmetric optical superlattices
• Anderson localization induced by complex potential

Cited by in corpus (14)

• Non-Hermitian Topological Phases: Principles and Prospects
• Encircling the Liouvillian exceptional points: a brief review
• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Engineering imaginary stark ladder in a dissipative lattice: passive $\mathcal{P}\mathcal{T}$ symmetry, K symmetry and localized damping
• Biorthogonal topological charge pumping in non-Hermitian systems
• Non-Hermitian skin effect in a single trapped ion
• Optical pumping through the Liouvillian skin effect
• Topology and its detection in a dissipative Aharonov-Bohm chain
• Digital Quantum Simulation of the Lindblad Master Equation and Its Nonlinear Extensions via Quantum Trajectory Averaging
• Optimal spectral transport of non-Hermitian systems
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Higher-order Liouvillian exceptional points in the dissipative dynamics of quadratic fermions