Measurement of Chern numbers through center-of-mass responses

Anno: 2016

Autori: Price HM., Zilberberg O., Ozawa T., Carusotto I., Goldman N.

Affiliazione autori: Univ Trento, INO CNR BEC Ctr, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, I-38123 Povo, Italy; ETH, Inst Theoret Phys, CH-8093 Zurich, Switzerland; Univ Libre Bruxelles, Fac Sci, CENOLI, B-1050 Brussels, Belgium.

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 four-dimensional quantum Hall effects. These results have important implications for experiments in engineered topological systems, such as ultracold gases and photonics.

Giornale/Rivista: PHYSICAL REVIEW B

Volume: 93 (24)      Da Pagina: 245113-1  A: 245113-16

Maggiori informazioni: The authors thank M. Aidelsburger, I. Bloch, J. Dalibard, M. Dalmonte, A. Dauphin, M. Lohse, S. Nascimbene, C. Schweizer, and D.-T. Tran for fruitful discussions. H.M.P., T.O., and I.C. are supported by the ERC through the QGBE grant, by the EU-FET Proactive grant AQuS, Project No. 640800, and by the Autonomous Province of Trento, partially through the project On silicon chip quantum optics for quantum computing and secure communications (SiQuro). H.M.P. was also supported by the EC through the H2020 Marie Sklodowska-Curie Action, Individual Fellowship Grant No. 656093 SynOptic. O.Z. ackno wledges the Swiss National Foundation for financial support. N.G. is financed by the FRS-FNRS Belgium and by the BSPO under PAI Project No. P7/18 DYGEST.
Parole chiavi: Quantized Hall Conductance; Topological Edge States; Magnetic Bloch Bands; Berry Phase; Thermodynamic Derivation; Semiclassical Dynamics; Hofstadter Spectrum; Ultracold Fermions; Field; Insulators
DOI: 10.1103/PhysRevB.93.245113

Citazioni: 65
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