, , , Hsin-I Lu, Lauren Aycock
Physical systems with non-trivial topological order find direct applications in metrology and promise future applications in quantum computing[2,3]. The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system's topology. At magnetic fields beyond the reach of current condensed matter experiment, around 10^4 Tesla, this conductance remains precisely quantized but takes on different values. Hitherto, quantized conductance has only been measured in extended 2-D systems. Here, we engineered and experimentally studied narrow 2-D ribbons, just 3 or 5 sites wide along one direction, using ultracold neutral atoms where such large magnetic fields can be engineered[6-11]. 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.
Bose-Einstein condensate, topology, Quantum-Hall