@article {valdes-curiel_topological_2021,
title = {Topological features without a lattice in {Rashba} spin-orbit coupled atoms},
journal = {Nat. Commun.},
volume = {12},
number = {1},
year = {2021},
note = {Place: HEIDELBERGER PLATZ 3, BERLIN, 14197, GERMANY Publisher: NATURE RESEARCH Type: Article},
month = {jan},
abstract = {Topological order can be found in a wide range of physical systems, from crystalline solids, photonic meta-materials and even atmospheric waves to optomechanic, acoustic and atomic systems. Topological systems are a robust foundation for creating quantized channels for transporting electrical current, light, and atmospheric disturbances. These topological effects are quantified in terms of integer-valued {\textquoteleft}invariants{\textquoteright}, such as the Chern number, applicable to the quantum Hall effect, or the Z2 invariant suitable for topological insulators. Here, we report the engineering of Rashba spin-orbit coupling for a cold atomic gas giving non-trivial topology, without the underlying crystalline structure that conventionally yields integer Chern numbers. We validated our procedure by spectroscopically measuring both branches of the Rashba dispersion relation which touch at a single Dirac point. We then measured the quantum geometry underlying the dispersion relation using matter-wave interferometry to implement a form of quantum state tomography, giving a Berry{\textquoteright}s phase with magnitude . This implies that opening a gap at the Dirac point would give two dispersions (bands) each with half-integer Chern number, potentially implying new forms of topological transport.Here, the authors study topology in spin-orbit coupled 87Rb atoms by using time domain spectroscopy and quantum state tomography. They measure full quantum state to extract the Berry phase of the system and show signatures of a half-integer Chern index.},
issn = {2041-1723},
doi = {10.1038/s41467-020-20762-4},
author = {Valdes-Curiel, A. and Trypogeorgos, D. and Liang, Q. -Y. and Anderson, R. P. and Spielman, I. B.}
}