Mapping the Berry curvature from semiclassical dynamics in optical lattices
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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.
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The time-reversal protocol comparing propagation under +φ0 and -φ0 separates Berry curvature from group velocity effects.
“To cleanly separate Berry curvature from group velocity effects, we apply a variant of the 'time-reversal' protocol 36 and compare the propagation (see Fig. 3a) under a reversal of the sign of the phase magnitude (that is, +ϕ 0 and -ϕ 0 ) to find”
From Experimental measurement of the Berry curvature from anomalous transport (2017) · cites this paper as [36]
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References 54 · Cited by 201
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- Authors
- Price, H. M., & Cooper, N. R.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2012-03-15
- Volume
- 85
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1986891238
- Cited by
- 201
- References
- 54
- Citations by year
- 2026: 1 · 2025: 9 · 2024: 6 · 2023: 10 · 2022: 16 · 2021: 12 · 2020: 14 · 2019: 9 · 2018: 19 · 2017: 14 · 2016: 15 · 2015: 16 · 2014: 31 · 2013: 21 · 2012: 8
- FWCI
- 12.56
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Engineering and Physical Sciences Research Council (EP/F032773/1)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Keywords
- Berry curvature, optical lattices, ultracold gases, semiclassical dynamics, Bloch oscillations, wave packet dynamics, Chern number, topological band structure
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