No abstract

Physical systems with non-trivial topological order find direct applications in metrology (Klitzing et al 1980 Phys. Rev. Lett. 45 494-7) and promise future applications in quantum computing (Freedman 2001 Found. Comput. Math. 1 183-204; Kitaev 2003 Ann. Phys. 303 2-30). The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system's topology (Laughlin 1981 Phys. Rev. B 23 5632-33). At magnetic fields beyond the reach of current condensed matter experiment, around 10 4 T, this conductance remains precisely quantized with values based on the topological order (Thouless et al 1982 Phys. Rev. Lett. 49 405-8). Hitherto, quantized conductance has only been measured in extended 2D systems. Here, we experimentally studied narrow 2D ribbons, just 3 or 5 sites wide along one direction, using ultracold neutral atoms where such large magnetic fields can be engineered (Jaksch and Zoller 2003 New J. Phys. 5 56; Miyake et al 2013 Phys. Rev. Lett. 111 185302; Aidelsburger et al 2013 Phys. Rev. Lett. 111 185301; Celi et al 2014 Phys. Rev. Lett. 112 043001; Stuhl et al 2015 Science 349 1514; Mancini et al 2015 Science 349 1510; An et al 2017 Sci. Adv. 3). We microscopically imaged the transverse spatial motion underlying the quantized Hall effect. Our measurements identify the topological Chern numbers with typical uncertainty of 5%, and show that although band topology is only properly defined in infinite systems, its signatures are striking even in nearly vanishingly thin systems.

The creation of particle-antiparticle pairs from vacuum by a large electric field is at the core of quantum electrodynamics. Despite the wide acceptance that this phenomenon occurs naturally when electric field strengths exceed E c ≈10 18 V m −1 , it has yet to be experimentally observed due to the limitations imposed by producing electric fields at this scale. The high degree of experimental control present in ultracold atomic systems allow experimentalists to create laboratory analogs to high-field phenomena. Here we emulated massive relativistic particles subject to large electric field strengths, thereby quantum-simulated particle-antiparticle pair creation, and experimentally explored particle creation from 'the Dirac vacuum'. Data collected from our analog system spans the full parameter regime from low applied field (negligible pair creation) below the Sauter-Schwinger limit, to high field (maximum rate of pair creation) far in excess of the Sauter-Schwinger limit. In our experiment, we perform direct measurements on an analog atomic system and show that this high-field phenomenon is well-characterized by Landau-Zener tunneling, well known in the atomic physics context, and we find full quantitative agreement with theory with no adjustable parameters.