Direct measurement of the Zak phase in topological Bloch bands

By M. Atala, M. Aidelsburger, J. Barreiro, D. Abanin, Takuya Kitagawa, E. Demler, I. Bloch. Nature Physics, 2012

940 citations recorded by the source corpus.

Geometric 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. In the band theory of solids, the topological properties of Bloch bands are characterized by geometric phases. For cold atoms moving in a one-dimensional optical potential the geometric phase can be measured directly using Bloch oscillations and Ramsey interferometry.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/5ef137edaacb0d4b752de53a1dad93c9ed910e78

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms (2014, neutral): “25(16)ErL, with Erα=~(2)k(2)α/(2m), α={s,L}.”
Floquet topological transitions in a driven one-dimensional topological insulator (2015, methodology): “Differences between Zak phases for topologically nontrivial systems in one dimension are quantized in units of π even though the value by itself depends on the choice of the unit cell [49].”
Topological bands for ultracold atoms (2018, neutral): “To establish the link between the winding of φZak and the transported mass, we start from the fact that the lattice remains at any time periodic, so that the Bloch theorem ensures that the quasi-momentum q is conserved during the evolution.”
Topological Thouless pumping of ultracold fermions (2015, methodology): “A pictorial understanding of this alternative pumping process is provided by the tight-binding Rice-Mele model [6, 20],”
Colloquium: Strong-field phenomena in periodic systems (2017, background): “Recent works have demonstrated the measurements of the Zak phase (Atala et al., 2013; Duca et al., 2015) and oscillations of effective mass of a particle in an optical lattice driven by external force (Chang et al., 2014).”
Probing non-Hermitian skin effect and non-Bloch phase transitions (2019, methodology): “Bulk dynamics in real space, such as in quantum walk experiments, is a powerful tool to provide useful information about topological invariants and edge states in synthetic topological matter [41–49].”
Topological characterization of chiral models through their long time dynamics (2017, background): “1D chiral topological insulators have been realized in numerous platforms as ultracold atoms [6, 11], photonic crystals [15], photonic quantum walks [21–25].”
Photonic quadrupole topological phases (2018, background): “In fact, topologically robust, localized 0D edge states in 1D systems and propagating 1D edge states in 2D systems have been realized using atomic [11–13], photonic [14–19] as well as phononic lattices [20–22].”
Topological characterizations of an extended Su–Schrieffer–Heeger model (2019, background): “It can be measured by detecting the phase of a particle across the Brillouin zone [66], and can also be measured with a quench dynamics [77].”