Talk given by

Prof. Dr. Oded Zilberberg

Quantum Engineered Systems

ETH Zürich

Zurich, Switzerland

Abstract:

In my talk, I will introduce the close relationship between the 2D quantum Hall effect and 
1D topological pumps. I will, then, present our recent experimental realizations of 
topological pumps using two completely different bosonic systems, namely, using coupled 
photonic waveguide arrays and with trapped atoms in optical superlattices. 

In the second part of my talk, I will detail the connection between quasicrystals and
topological pumps. In this context, we have found that quasicrystals inherit topological
attributes from their corresponding pumps, i.e., quasicrystals are characterized with
topological indices from dimensions higher than their own. I will discuss several 1D
quasiperiodic models with nontrivial 1st Chern numbers and topological boundary states, 
which are inherited from their corresponding topological pumps. 

Last, I will present how this naturally leads to realizing the 4D and 6D quantum Hall
effects, and correspondingly  2D and 3D topological pumps in the lab. Both the 4D 
topological bulk response and its associated boundary phenomena were realized recently 
using trapped atoms in optical superlattices and photonic waveguide arrays, respectively. 
The connection between topological pumps and higer-dimensional quantum Hall models 
offers a natural interpretation for high-order topological insulators. 

Figure Caption: 

An illustration of two experimental realizations of a 2D topological pump, which is a 
dynamical realization of the 4D quantum Hall effect. Top: a 2D array of coupled photonic 
waveguides where the topological boundary phenomena is studied. Bottom: trapped cold 
atoms in a 2D optical lattice. Center: A tesseract demonstrating a 2D projection of a 
4D hypercube.