Atala, MarcosAidelsburger, MonikaBarreiro, Julio T.Abanin, DmitryKitagawa, TakuyaDemler, EugeneBloch, Immanuel2014-05-052013Atala, Marcos, Monika Aidelsburger, Julio T. Barreiro, Dmitry Abanin, Takuya Kitagawa, Eugene Demler, and Immanuel Bloch. 2013. “Direct Measurement of the Zak Phase in Topological Bloch Bands.” Nat Phys 9 (12) (November 3): 795–800.1745-2473http://nrs.harvard.edu/urn-3:HUL.InstRepos:12150777Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the band theory of solids. Here we report on the measurement of the geometric phase acquired by cold atoms moving in one-dimensional optical lattices. Using a combination of Bloch oscillations and Ramsey interferometry, we extract the Zak phase—the Berry phase gained during the adiabatic motion of a particle across the Brillouin zone—which can be viewed as an invariant characterizing the topological properties of the band. For a dimerized lattice, which models polyacetylene, we measure a difference of the Zak phase δφZak = 0.97(2)π for the two possible polyacetylene phases with different dimerization. The two dimerized phases therefore belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. Our work establishes a new general approach for probing the topological structure of Bloch bands inoptical lattices.en-USJournal Article2013-10-04Marcos Atala, Monika Aidelsburger, Julio T. Barreiro, Dmitry Abanin, Takuya Kitagawa, Eugene Demler, Immanuel Bloch2014-05-0610.1038/nphys2790