Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit

Xinsheng Tan, Dan-Wei Zhang, Zhen Yang, Ji Chu, Yan-Qing Zhu, Danyu Li, Xiaopei Yang, Shuqing Song, Zhikun Han, Zhiyuan Li, Yuqian Dong, Hai-Feng Yu, Hui Yan, Shi-Liang Zhu, and Yang Yu

Phys. Rev. Lett. 122, 210401 – Published 29 May 2019; Erratum Phys. Rev. Lett. 123, 159902 (2019)

Abstract

A Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable superconducting circuits, we experimentally demonstrate two methods to directly measure the quantum metric tensor for characterizing the geometry and topology of underlying quantum states in parameter space. The first method is to probe the transition probability after a sudden quench, and the second one is to detect the excitation rate under weak periodic driving. Furthermore, based on quantum metric and Berry-curvature measurements, we explore a topological phase transition in a simulated time-reversal-symmetric system. The work opens up a unique approach to explore the topology of quantum states with the QGT.

Received 4 February 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.210401

Physics Subject Headings (PhySH)

Geometric & topological phases Quantum simulation

Superconducting qubits

Quantum Information, Science & TechnologyGeneral Physics

Erratum

Erratum: Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit [Phys. Rev. Lett. 122, 210401 (2019)]

Xinsheng Tan, Dan-Wei Zhang, Zhen Yang, Ji Chu, Yan-Qing Zhu, Danyu Li, Xiaopei Yang, Shuqing Song, Zhikun Han, Zhiyuan Li, Yuqian Dong, Hai-Feng Yu, Hui Yan, Shi-Liang Zhu, and Yang Yu

Phys. Rev. Lett. 123, 159902 (2019)

Authors & Affiliations

Xinsheng Tan^1,*, Dan-Wei Zhang^2,†, Zhen Yang¹, Ji Chu¹, Yan-Qing Zhu¹, Danyu Li¹, Xiaopei Yang¹, Shuqing Song¹, Zhikun Han¹, Zhiyuan Li¹, Yuqian Dong¹, Hai-Feng Yu¹, Hui Yan², Shi-Liang Zhu^1,2,‡, and Yang Yu^1,§

¹National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
²Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China