Mapping the Berry curvature from semiclassical dynamics in optical lattices

By H. Price, N. Cooper. 2011

140 citations recorded by the source corpus.

We propose a general method by which experiments on ultracold gases can be used to determine the topological properties of the energy bands of optical lattices, as represented by the map of the Berry curvature across the Brillouin zone. The Berry curvature modifies the semiclassical dynamics and hence the trajectory of a wave packet undergoing Bloch oscillations. However, in two dimensions these trajectories may be complicated Lissajous-like figures, making it difficult to extract the effects of Berry curvature in general. We propose how this can be done using a "time-reversal" protocol. This compares the velocity of a wave packet under positive and negative external force, and allows a clean measurement of the Berry curvature over the Brillouin zone. We discuss how this protocol may be implemented and explore the semiclassical dynamics for three specific systems: the asymmetric hexagonal lattice, and two "optical flux" lattices in which the Chern number is nonzero. Finally, we discuss general experimental considerations for observing Berry curvature effects in ultracold gases.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/769a447d1a4318f6e03a9322e67cad152dfd6c33

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Topological bands for ultracold atoms (2018, unknown): “As a result of this contribution, the recording of a given trajectory inside the Brillouin zone allows one to reconstruct the Berry curvature along this trajectory (Price and Cooper, 2012).”
Direct measurement of the Zak phase in topological Bloch bands (2012, unknown): “Recently, it has also been suggested that in the context of ultra-cold atoms, topological properties could be studied through time-of-ﬂight images ( 17–19 ) or measurements of anomalous velocity ( 6,20 ).”
Topological quantum matter with ultracold gases in optical lattices (2016, background): “In cold gases, various physical signatures of the Berry curvature can be probed: For instance, the anomalous (transverse) velocity of a wave-packet under the action of a force [41], or the Aharonov-Bohm phase acquired by a wave-packet performing a loop in k-space (reflecting that the Berry curvature”
Realization of an anomalous Floquet topological system with ultracold atoms (2020, background): “The Berry curvature acts as an effective magnetic field in quasimomentum-space, adding a transverse component to the atom’s velocity [14, 18, 46, 47].”
Topological photonics (2018, methodology): “…by Wimmer et al. (2017) of the k-space distribution of the bulk Berry curvature from the anomalous velocity of a wave packet performing Bloch oscillations under an external force as theoretically proposed by Dudarev et al. (2004), Price and Cooper (2012), and Cominotti and Carusotto (2013).”
Experimental realization of the topological Haldane model with ultracold fermions (2014, background): “Subtracting the result for the opposite gradient gives the differential drift D, which provides more direct access to the Berry-curvature distribution [25].”
Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields (2014, unknown): “[87–90]).”
Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms (2014, methodology): “4b, see Supplementary Information).”