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

  1. Xinsheng Tan,
  2. Dan-Wei Zhang,
  3. Zhen Yang,
  4. Ji Chu,
  5. Yan-Qing Zhu,
  6. Danyu Li,
  7. Xiaopei Yang,
  8. Shuqing Song,
  9. Zhikun Han,
  10. Zhiyuan Li,
  11. Yuqian Dong,
  12. Hai-Feng Yu,
  13. Hui Yan,
  14. Shi-Liang Zhu,
  15. and Yang Yu
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, which is characterized by the Euler characteristic number instead of the Chern number. The work opens up a unique approach to explore the topology of quantum states with the QGT.

Topological Maxwell Metal Bands in a Superconducting Qutrit

  1. Xinsheng Tan,
  2. Dan-Wei Zhang,
  3. Qiang Liu,
  4. Guangming Xue,
  5. Hai-Feng Yu,
  6. Yan-Qing Zhu,
  7. Hui Yan,
  8. Shi-Liang Zhu,
  9. and Yang Yu
We experimentally explore the topological Maxwell metal bands by mapping the momentum space of condensed-matter models to the tunable parameter space of superconducting quantum circuits.
An exotic band structure that is effectively described by the spin-1 Maxwell equations is imaged. Three-fold degenerate points dubbed Maxwell points are observed in the Maxwell metal bands. Moreover, we engineer and observe the topological phase transition from the topological Maxwell metal to a trivial insulator, and report the first experiment to measure the Chern numbers that are higher than one.