Experimental Observation of Tensor Monopoles with a Superconducting Qudit.

Monopoles play a center role in gauge theories and topological matter. There are two fundamental types of monopoles in physics: vector monopoles and tensor monopoles. Examples of vector monopoles include the Dirac monopole in three dimensions and Yang monopole in five dimensions, which have been extensively studied and observed in condensed matter or artificial systems. However, tensor monopoles are less studied, and their observation has not been reported. Here we experimentally construct a tunable spin-1 Hamiltonian to generate a tensor monopole and then measure its unique features with superconducting quantum circuits. The energy structure of a 4D Weyl-like Hamiltonian with threefold degenerate points acting as tensor monopoles is imaged. Through quantum-metric measurements, we report the first experiment that measures the Dixmier-Douady invariant, the topological charge of the tensor monopole. Moreover, we observe topological phase transitions characterized by the topological Dixmier-Douady invariant, rather than the Chern numbers as used for conventional monopoles in odd-dimensional spaces.

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

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.

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

This corrects the article DOI: 10.1103/PhysRevLett.122.210401.

Synthesis and Surface Strengthening Modification of Silica Aerogel from Fly Ash.

This study focuses on using activated fly ash to preparate silica aerogel by the acid solution-alkali leaching method and ambient pressure drying. Additionally, to improve the performance of silica aerogel, C6H16O3Si (KH-570) and CH3Si(CH3O)3 (MTMS) modifiers were used. Finally, this paper investigated the factors affecting the desilication rate of fly ash and analyzed the structure and performance of silica aerogel. The experimental results show that: (1) The factors affecting the desilication rate are ranked as follows: hydrochloric acid concentration > solid-liquid ratio > reaction temperature > reaction time. (2) KH-570 showed the best performance, and when the volume ratio of the silica solution to it was 10:1, the density of silica aerogel reached a minimum of 183 mg/cm3. (3) The optimal process conditions are a hydrochloric acid concentration of 20 wt%, a solid-liquid ratio of 1:4, a reaction time of two hours, and a reaction temperature of 100 °C. (4) The optimal performance parameters of silica aerogel were the thermal conductivity, specific surface area, pore volume, average pore size, and contact angle values, with 0.0421 W·(m·K)-1, 487.9 m2·g-1, 1.107 cm3·g-1, 9.075 nm, and 123°, respectively. This study not only achieves the high-value utilization of fly ash, but also facilitates the effective recovery and utilization of industrial waste.