title: Four-Dimensional Quantum Hall Effect with Ultracold Atoms.
abstract: 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. Our proposal sets the stage for the exploration of novel topological phases in higher dimensions.
authors.affiliation: INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, I-38123 Povo, Italy.
authors.forename: H M
authors.initials: HM
authors.lastname: Price
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland.
authors.forename: O
authors.initials: O
authors.lastname: Zilberberg
authors.affiliation: INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, I-38123 Povo, Italy.
authors.forename: T
authors.initials: T
authors.lastname: Ozawa
authors.affiliation: INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, I-38123 Povo, Italy.
authors.forename: I
authors.initials: I
authors.lastname: Carusotto
authors.affiliation: CENOLI, Faculté des Sciences, Université Libre de Bruxelles (U.L.B.), B-1050 Brussels, Belgium.
authors.forename: N
authors.initials: N
authors.lastname: Goldman