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arXiv:1410.4484 · Europhysics Letters (EPL)

Interferometric detection of Chern numbers of Haldane model on bosonic optical lattices

Jian Xu

Published Nov 1, 2015• 0 citations
arXivHTMLPDF

Abstract

Topological states of matter emerge as a new type of quantum phases, which can be distinguished by their associated topological invariants, e.g. , Chern numbers. Currently, there has been increasing interest toward the physical detection of the new predicted topological phases. Here, we propose an interferometric approach to directly measure the Chern number of the topological Haldane model in bosonic optical lattices via detecting the associated Zak phases. We show that this interferometric approach can distinguish Zak phases of from 0 in the first Brillouin zone, and thus it provides a new tool to directly detect the Chern number of topological systems. In addition, we demonstrate that this method is feasible under realistic experimental conditions and may generalize to detect topological systems with higher Chern numbers.

DOI
10.1209/0295-5075/112/46001

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Recently, optical lattices with nonzero Berry's phases of Bloch bands have been realized. New approaches for measuring Berry's phases and topological properties of bands with experimental tools appropriate for ultracold atoms need to be developed. In this Letter, we propose an interferometric method for measuring Berry's phases of two-dimensional Bloch bands. The key idea is to use a combination of Ramsey interference and Bloch oscillations to measure Zak phases, i.e., Berry's phases for closed trajectories corresponding to reciprocal lattice vectors. We demonstrate that this technique can be used to measure the Berry curvature of Bloch bands, the π Berry's phase of Dirac points, and the first Chern number of topological bands. We discuss several experimentally feasible realizations of this technique, which make it robust against low-frequency magnetic noise.
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Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic for neutral atoms. By establishing a natural correspondence between the time-reversal invariant topological insulator and the quantum anomalous Hall system, we show for a class of Chern insulators that the topology can be determined by only measuring Bloch eigenstates at highly symmetric points of the Brillouin zone. Furthermore, we introduce two experimental schemes, including the spin-resolved Bloch oscillation, to carry out the measurement. These schemes are highly feasible under realistic experimental conditions. Our results may provide a powerful tool to detect topological phases in cold atoms.
Topological invariants, such as the Chern number, characterize topological phases of matter. Here we provide a method to detect Chern numbers in systems with two distinct species of fermion, such as spins, orbitals or several atomic states. We analytically show that the Chern number can be decomposed as a sum of component specific winding numbers, which are themselves physically observable. We apply this method to two systems, the quantum spin Hall insulator and a staggered topological superconductor, and show that (spin) Chern numbers are accurately reproduced. The measurements required for constructing the component winding numbers also enable one to probe the entanglement spectrum with respect to component partitions. Our method is particularly suited to experiments with cold atoms in optical lattices where time-of-flight images can give direct access to the relevant observables.