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Studying band-topology with ultracold fermions in an optical lattice: Experimental realisation of the Haldane model

Gregor Jotzu, Michael Messer, Rémi Desbuquois, Martin Lebrat, Thomas Uehlinger, Daniel Greif, Tilman Esslinger

Published Nov 1, 2015• 0 citations
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Bulletin of the American Physical Society•Jun 6, 2012•0 citations
We propose an experimental scheme to directly detect the Chern number of the topological Haldane model realized with optical lattices based on the time-of-flight imaging. The Haldane model can be realized with two-component fermionic atoms loaded in the optical lattices consisting of two sublattices and each of the sublattices hosts atoms with a specific component of the atoms. We find that the Bloch wave function of the lower band can be measured with the time-of-flight imaging and thus the Chern number can be directly obtained from the Bloch function. We numerically simulate the Chern number of the Haldane model and its modified version in both honeycomb lattice and brick-wall lattice, and show that the proposed approach is general and feasible in practical experiments.
We consider ultracold atoms in a two-dimensional optical lattice of the dice geometry in a tight-binding regime. The atoms experience a laser-assisted tunneling between the nearest neighbor sites of the dice lattice accompanied by the momentum recoil. This allows one to engineer staggered synthetic magnetic fluxes over plaquettes, and thus pave a way towards the realization of topologically nontrivial band structures. In such a lattice the real-valued next-nearest neighbor transitions are not needed to reach a topological regime. Yet, such transitions can increase a variety of the obtained topological phases. The dice lattice represents a triangular Bravais lattice with a three-site basis consisting of a hub site connected to two rim sites. As a consequence, the dice lattice supports three energy bands. From this point of view, our model can be interpreted as a generalization of the paradigmatic Haldane model which is reproduced if one of the two rim sublattices is eliminated. We demonstrate that the proposed upgrade of the Haldane model creates a significant added value, including an easy access to topological semimetal phases relying only on the nearest neighbor coupling, as well as enhanced topological band structures featuring Chern numbers higher than one leading to physics beyond the usual quantum Hall effect. The numerical investigation is supported and complemented by an analytical scheme based on the study of singularities in the Berry connection.