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Measurement of Chern numbers through center-of-mass responses
Quantum Gases · Submitted 4 Feb 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this work, we show how such center-of-mass observables can have a much richer dependence on topological invariants than previously discussed.
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The abstract, sentence by sentence
Probing the center-of-mass of an ultracold atomic cloud can be used to measure Chern numbers, the topological invariants underlying the quantum Hall effects. In this work, we show how such center-of-mass observables can have a much richer dependence on topological invariants than previously discussed. In fact, the response of the center of mass depends not only on the current density, typically measured in a solid-state system, but also on the particle density, which itself can be sensitive to the topology of the band structure. We apply a semiclassical approach, supported by numerical simulations, to highlight the key differences between center-of-mass responses and more standard conductivity measurements. We illustrate this by analyzing both the two- and the four-dimensional quantum Hall effects. These results have important implications for experiments in engineered topological systems, such as ultracold gases and photonics.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Probing the center-of-mass of an ultracold atomic cloud can be used to measure Chern numbers, the topological invariants underlying the quantum Hall effects. | background 0.98 | 0.12 | 0.24 | asserted 0.58 |
| s1 | In this work, we show how such center-of-mass observables can have a much richer dependence on topological invariants than previously discussed. | contribution 0.87 | 0.86 | 0.35 | asserted 1.00 |
| s2 | In fact, the response of the center of mass depends not only on the current density, typically measured in a solid-state system, but also on the particle density, which itself can be sensitive to the topology of the band structure. | result 0.83 | 0.62 | 0.33 | asserted 1.00 |
| s3 | We apply a semiclassical approach, supported by numerical simulations, to highlight the key differences between center-of-mass responses and more standard conductivity measurements. | method 0.98 | 0.93 | 0.08 | asserted 0.95 |
| s4 | We illustrate this by analyzing both the two- and the four-dimensional quantum Hall effects. | contribution 0.79 | 0.87 | 0.07 | asserted 0.92 |
| s5 | These results have important implications for experiments in engineered topological systems, such as ultracold gases and photonics. | interpretation 1.00 | 0.36 | 0.17 | asserted 0.96 |
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Original abstract
Probing the center-of-mass of an ultracold atomic cloud can be used to measure Chern numbers, the topological invariants underlying the quantum Hall effects. In this work, we show how such center-of-mass observables can have a much richer dependence on topological invariants than previously discussed. In fact, the response of the center of mass depends not only on the current density, typically measured in a solid-state system, but also on the particle density, which itself can be sensitive to the topology of the band structure. We apply a semiclassical approach, supported by numerical simulations, to highlight the key differences between center-of-mass responses and more standard conductivity measurements. We illustrate this by analyzing both the two- and the four-dimensional quantum Hall effects. These results have important implications for experiments in engineered topological systems, such as ultracold gases and photonics.
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2 arXiv papers cite this in 2 sentences
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Cites it as background 1 paper
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A complete discussion of the subtle features relating the spatial shift of the center of mass of the intensity distribution to the more usual concept of Hall current can be found in our recent paper [ref] .
Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics · Derivation of the driven-dissipative 4D quantum Hall formula · 0.86
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