2020/01/31 by Boxiang Wang, B. X. Wang, Changying Zhao +1 · 11 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Dipole #Mathematics #Physics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Quantum phases #Quasiperiodic function #Quasiperiodicity #Symmetry protected topological order #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #Ultracold atom #physics.atom-ph #physics.optics #quant-ph
paper · pdf · doi:10.1103/physreva.103.013727
published in Physical Review A 103(1) (American Physical Society) · Final version, 15 pages, 10 figures, comments are welcome
arxiv created 2021/01/13 · openalex publication_date 2021/01/28 · arxiv updated 2021/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Topological quantum optical states in one-dimensional (1D) quasiperiodic cold atomic chains are studied in this work. We propose that by introducing incommensurate modulations on the interatomic distances of 1D periodic atomic chains, the off-diagonal Aubry-Andr'e-Harper (AAH) model can be mimicked, although the crucial difference is the existence of long-range dipole-dipole interactions. The discrete band structures with respect to the modulation phase, which plays the role of a dimension extension parameter, are calculated for finite chains beyond the nearest-neighbor approximation. It is found that the present system indeed supports nontrivial topological states localized over the boundaries. Despite the presence of long-range dipole-dipole interactions that leads to an asymmetric band structure, it is demonstrated that this system inherits the topological properties of two-dimensional integer quantum Hall systems. The spectral position, for both real and imaginary frequencies, and number of these topologically protected edge states are still governed by the gap-labeling theorem and characterized by the topological invariant, namely, the (first) Chern number, indicating the validity of bulk-boundary correspondence. Due to the fractal spectrum arising from the quasiperiodicity in a substantially wide range of system parameters, our system provides a large number of topological gaps and optical states readily for practical use. It is also revealed that a substantial proportion of the topological edge states are highly subradiant with extremely low decay rates, which therefore offer an appealing route for controlling the emission of external quantum emitters and achieving high-fidelity quantum state storage.