Imaging topology of Hofstadter ribbons.

Physical systems with non-trivial topological order find direct applications in metrology (Klitzing 1980 494-7) and promise future applications in quantum computing (Freedman 2001 183-204; Kitaev 2003 2-30). The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system's topology (Laughlin 1981 B 5632-33). At magnetic fields beyond the reach of current condensed matter experiment, around 10 T, this conductance remains precisely quantized with values based on the topological order (Thouless 1982 405-8).

Brownian motion of solitons in a Bose-Einstein condensate.

We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated [Formula: see text] Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability.