Four-Dimensional Quantum Hall Effect with Ultracold Atoms

Year: 2015

Authors: Price HM., Zilberberg O., Ozawa T., Carusotto I., Goldman N.

Autors Affiliation: Univ Trento, INO CNR BEC Ctr, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, I-38123 Povo, Italy; ETH, Inst Theoret Phys, CH-8093 Zurich, Switzerland; Univ Libre Bruxelles, Fac Sci, CENOLI, B-1050 Brussels, Belgium.

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.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 115 (19)      Pages from: 195303-1  to: 195303-6

More Information: We thank N. R. Cooper, J. Dalibard, A. Celi, I. Bloch, M. Aidelsburger, C. Weitenberg, L. Fallani, P. Massignan, M. Lewenstein, A. Dauphin, P. Gaspard, J. Catani, C. Sias, L. Mazza, K. Kraus, and Z. Ringel for fruitful discussions. H. M. P., T. O. and I. C. were funded by ERC through the QGBE grant, by the EU-FET Proactive grant AQuS (Project No. 640800), and by Provincia Autonoma di Trento, partially through the project On silicon chip quantum optics for quantum computing and secure communications-SiQuro. O. Z. acknowledges the Swiss National Foundation for financial support. N. G. is financed by the FRS-FNRS Belgium and by the BSPO under the PAI project P7/18 DYGEST.
KeyWords: Magnetic Bloch Bands; Berry Phase; Gauge-fields; Thermodynamic Derivation; Topological Insulators; Semiclassical Dynamics; Hofstadter Spectrum; Edge States; Fermions; Hyperorbits
DOI: 10.1103/PhysRevLett.115.195303

Citations: 184
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