Topological features without a lattice in Rashba spin-orbit coupled atoms

• Published in: Nature communications Vol. 12; no. 1; p. 593
• Main Authors: Valdés-Curiel, A., Trypogeorgos, D., Liang, Q.-Y., Anderson, R. P., Spielman, I. B.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 26.01.2021; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/119/2792; 639/766/483/3926; Atmospheric disturbances; Cold spinning; Crystal structure; Crystallinity; Humanities and Social Sciences; Integers; Interferometry; Invariants; Metamaterials; multidisciplinary; Photonic crystals; Quantum Hall effect; Quantum mechanics; S phase; Science; Science (multidisciplinary); Spectroscopy; Spin-orbit interactions; Tomography; Topological insulators; Topology
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-020-20762-4

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 ‘invariants’, such as the Chern number, applicable to the quantum Hall effect, or the Z 2 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’s phase with magnitude π . 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.