Direct Measurement of the Zak Phase in Topological Bloch Bands
Figure reprinted by permission from Macmillan Publishers Ltd: Nature ©2013
Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the band theory of solids.
Professor Eugene Demler and colleagues from Harvard, Ludwig-Maximilians-Universität, Max-Planck Institute of Quantum Optics, and Rakuten, Inc. (Japan) reported on the measurement of the geometric phase acquired by cold atoms moving in one-dimensional optical lattices in Nature Physics. Using a combination of Bloch oscillations and Ramsey interferometry, their extracted 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, their measured a difference of the Zak phase δφZak = 0.97(2)π for the two possible polyacetylene phases with different dimerization. They concluded that the two dimerized phases therefore belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. This work establishes a new general approach for probing the topological structure of Bloch bands inoptical lattices.
See M. Atala, M. Aidelsburger, J.T. Barreiro, D. Abanin, T. Kitagawa, E. Demler & I. Bloch, "Direct measurement of the Zak phase in topological Bloch bands," Nature Physics (published online 03 November 2013) | doi:10.1038/nphys2790.