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  • Letter
  • Open Access

Extracting the quantum geometric tensor of an optical Raman lattice by Bloch-state tomography

Chang-Rui Yi1,2,3,*, Jinlong Yu4,5,*, Huan Yuan1,2,3, Rui-Heng Jiao1,2,3, Yu-Meng Yang1,2,3, Xiao Jiang1,2,3, Jin-Yi Zhang1,2,3, Shuai Chen1,2,3, and Jian-Wei Pan1,2,3

  • 1Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
  • 2Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
  • 3Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
  • 4Center for Theoretical Physics, Hainan University, Haikou 570228, China
  • 5School of Science, Hainan University, Haikou 570228, China

  • *These authors contributed equally to this work.
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Phys. Rev. Research 5, L032016 – Published 2 August, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032016

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 whose real part is the quantum metric tensor. Here, we experimentally realize a complete Bloch-state tomography to directly measure the 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. Furthermore, we experimentally test a predicted inequality between the Berry curvature and the quantum metric tensor, which reveals a deep connection between the topology and geometry.

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Phys. Rev. Research 5, L032016– Published 2 August, 2023
  • Received 28 June 2022
  • Accepted 12 July 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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