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Extracting the Quantum Geometric Tensor of an Optical Raman Lattice by Bloch State Tomography

Authors :
Yi, Chang-Rui
Yu, Jinlong
Yuan, Huan
Jiao, Rui-Heng
Yang, Yu-Meng
Jiang, Xiao
Zhang, Jin-Yi
Chen, Shuai
Pan, Jian-Wei
Source :
Phys. Rev. Research 5, L032016 (2023)
Publication Year :
2023

Abstract

In Hilbert space, the geometry of the quantum state is identified by the quantum geometric tensor (QGT), whose imaginary part is the Berry curvature and real part is the quantum metric tensor. Here, we propose and experimentally implement a complete Bloch state tomography to directly measure eigenfunction of an optical Raman lattice for ultracold atoms. Through the measured eigenfunction, the distribution of the complete QGT in the Brillouin zone is reconstructed, with which the topological invariants are extracted by the Berry curvature and the distances of quantum states in momentum space are measured by the quantum metric tensor. Further, we experimentally test a predicted inequality between the Berry curvature and quantum metric tensor, which reveals a deep connection between topology and geometry.

Details

Database :
arXiv
Journal :
Phys. Rev. Research 5, L032016 (2023)
Publication Type :
Report
Accession number :
edsarx.2301.06090
Document Type :
Working Paper
Full Text :
https://doi.org/10.1103/PhysRevResearch.5.L032016