# Quantum metric of topological and non-topological insulators in AMO and other systems

- Date
- December 20 at 13:30 - 15:00, 2021 (JST)

- Speaker
- Dr. Tomoki Ozawa (Associate Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)

- Venue
- via Zoom

- Language
- English

Recently, the concept of quantum geometry is attracting great interests in various areas of condensed matter and AMO physics. Quantum geometry tells how much the quantum states "change" as one moves in a parameter space, and is closely related to the topology of the quantum states. Quantum geometric tensor is often used to characterize the geometry, whose real part is the quantum metric and the imaginary part is the Berry curvature. Although Berry curvature is rather well-studied in the context of topological insulators and superconductors, less has been known about the quantum metric. However, experiments detecting the quantum metric have appeared in the past couple of years and interest in quantum metric is indeed growing. In this talk, I first explain basics of quantum metric and its recent experimental observations. I then discuss various aspects of quantum metric, including its relation to localization, topology, and the Kähler geometry.

*If you would like to participate, please contact Hidetoshi Taya.

## References

- Tomoki Ozawa and Nathan Goldman, Extracting the quantum metric tensor through periodic driving, Phys. Rev. B 97, 201117(R) (2018), doi: 10.1103/PhysRevB.97.201117
- Tomoki Ozawa and Nathan Goldman, Probing localization and quantum geometry by spectroscopy, Phys. Rev. Research 1, 032019(R) (2019), doi: 10.1103/PhysRevResearch.1.032019
- Luca Asteria, Duc Thanh Tran, Tomoki Ozawa, Matthias Tarnowski, Benno S. Rem, Nick Fläschner, Klaus Sengstock, Nathan Goldman and Christof Weitenberg , Measuring quantized circular dichroism in ultracold topological matter, Nature Physics volume 15, pages 449–454 (2019), doi: 10.1038/s41567-019-0417-8
- Min Yu, Pengcheng Yang, Musang Gong, Qingyun Cao, Qiuyu Lu, Haibin Liu, Shaoliang Zhang, Martin B Plenio, Fedor Jelezko, Tomoki Ozawa, Nathan Goldman, Jianming Cai, Experimental measurement of the quantum geometric tensor using coupled qubits in diamond, National Science Review, Volume 7, Issue 2 (2020), doi: 10.1093/nsr/nwz193
- Tomoki Ozawa and Bruno Mera, Relations between topology and the quantum metric for Chern insulators, Phys. Rev. B 104, 045103 (2021), doi: 10.1103/PhysRevB.104.045103
- Bruno Mera and Tomoki Ozawa, Kähler geometry and Chern insulators: Relations between topology and the quantum metric, Phys. Rev. B 104, 045104 (2021), doi: 10.1103/PhysRevB.104.045104
- Bruno Mera and Tomoki Ozawa, Engineering geometrically flat Chern bands with Fubini-Study Kähler structure, Phys. Rev. B 104, 115160 (2021), doi: 10.1103/PhysRevB.104.115160
- Yu Liu, Min Yu, Pengcheng Yang, Musang Gong, Qingyun Cao, Shaoliang Zhang, Haibin Liu, Markus Heyl, Tomoki Ozawa, Nathan Goldman, Jianming Cai, Saturating the quantum Cramér-Rao bound and measuring the related quantum Fisher information in a nitrogen-vacancy center in diamond, Quantum Physics (2020), arxiv: 2003.08373