Topology in quasicrystals

Topological phases of matter have sparked an immense amount of activity in recent decades. Topological materials are classified by topological invariants that act as a non-local order parameter for any symmetry and condition. As a result, they exhibit quantized bulk and boundary observable phenomena, motivating various applications that are robust to perturbations. In this review, we explore such a topological classification for quasiperiodic systems, and detail recent experimental activity in the field.Comment: 14 pages, 6 figures, contribution to feature issue "Photonic Topological Materials" in Optical Materials Express, comments are welcom

Charge sensing amplification via weak values measurement

A protocol employing weak values (WVs) to obtain ultra sensitive amplification of weak signals in the context of a solid state setup is proposed. We consider an Aharonov-Bohm interferometer where both the orbital and the spin degrees of freedom are weakly affected by the presence of an external charge to be detected. The interplay between the spin and the orbital WVs leads to a significant amplification even in the presence of finite temperature, voltage, and external noise.Comment: 6 pages, 5 figure

The 6D quantum Hall effect and 3D topological pumps

Modern technological advances allow for the study of systems with additional synthetic dimensions. Using such approaches, higher-dimensional physics that was previously deemed to be of purely theoretical interest has now become an active field of research. In this work, we derive from first principles using a semiclassical equation of motions approach, the bulk response of a six-dimensional Chern insulator. We find that in such a system a quantized bulk response appears with a quantization originating from a six-dimensional topological index -- the 3rd Chern number. Alongside this novel six-dimensional response, we rigorously describe the lower even-dimensional Chern-like responses that can occur due to nonvanishing 1st and 2nd Chern numbers in sub-spaces of the six-dimensional space. Last, we propose how to realize such a bulk response using three-dimensional topological charge pumps in cold atomic systems.Comment: 12 pages + 13 pages of supporting material, 2 figures, published versio

High-order topological insulators from high-dimensional Chern insulators

Topological insulators are a novel state of matter that share a common feature: their spectral bands are associated with a nonlocal integer-valued index, commonly manifesting through quantized bulk phenomena and robust boundary effects. In this work, we demonstrate using dimensional reduction that high-order topological insulators are descendants from a chiral semimetal in higher dimensions. Specifically, we analyze the descendants of an ancestor four-dimensional Chern insulator in the limit where it becomes chiral and show their relation to two-dimensional second-order topological insulators. Correspondingly, the quantization of the charge accumulation at the corners of the 2D descendants is obtained and related to the topological indices -- the 1st and 2nd Chern numbers -- of the ancestor model. Our approach provides a connection between the boundary states of high-order topological insulators and topological pumps -- the latter being dynamical realizations of high-dimensional Chern insulators.Comment: 5 pages, 3 figures + supplementary material (8 pages), comments are welcom

Dynamical gauge fields with bosonic codes

The quantum simulation of dynamical gauge field theories offers the opportunity to study complex high-energy physics with controllable low-energy devices. For quantum computation, bosonic codes promise robust error correction that exploits multi-particle redundancy in bosons. In this Letter, we demonstrate how bosonic codes can be used to simulate dynamical gauge fields. We encode both matter and dynamical gauge fields in a network of resonators that are coupled via three-wave-mixing. The mapping to a $\mathbb{Z}_2$ dynamical lattice gauge theory is established when the gauge resonators operate as Schr\"odinger cat states. We explore the optimal conditions under which the system preserves the required gauge symmetries. Our findings promote realising high-energy models using bosonic codes.Comment: Includes Supplemental Materia