# Four-Dimensional Quantum Hall Effect with Ultracold Atoms

Hannah Price, University of Trento

09.12.2015 at 14:00

We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms. Based on contemporary technology, motion along a synthetic fourth dimension can be accomplished through controlled transitions between internal states of atoms arranged in a 3D optical lattice. From a semiclassical analysis, we identify the linear and nonlinear quantized current responses of our 4D model, relating these to the topology of the Bloch bands. We then propose experimental protocols, based on current or center-of-mass-drift measurements, to extract the topological second Chern number. Finally, we also briefly introduce how to include synthetic dimensions in integrated photonics, where these ideas may have practical applications in creating optical isolators and higher-dimensional photonic lattices.

H 107, Schellingstr. 4