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arXiv:2402.16070 · Physical Review Letters

High-Order Topological Pumping on a Superconducting Quantum Processor

Cheng-Lin Deng, Yu Liu, Yu-Ran Zhang, Xuegang Li, Tao Liu, Chi-Tong Chen, Tong Liu, Congwei Lu, Yong-Yi Wang, Tianming Li, Cai-Ping Fang, Si-Yun Zhou, Jia-Cheng Song, Yue-Shan Xu, Yang He, Zheng-He Liu, Kaixuan Huang, Zhongcheng Xiang, Jieci Wang, Dongning Zheng, Guangming Xue, Kai Xu, Haifeng Yu, Heng Fan

Published Oct 1, 2024• 15 citations
arXivHTMLPDF

Abstract

High-order topological phases of matter refer to the systems of n-dimensional bulk with the topology of m-th order, exhibiting (n-m)-dimensional boundary modes and can be characterized by topological pumping. Here, we experimentally demonstrate two types of second-order topological pumps, forming four 0-dimensional corner localized states on a 4×4 square lattice array of 16 superconducting qubits. The initial ground state of the system at half-filling, as a product of four identical entangled 4-qubit states, is prepared using an adiabatic scheme. During the pumping procedure, we adiabatically modulate the superlattice Bose-Hubbard Hamiltonian by precisely controlling both the hopping strengths and on-site potentials. At the half pumping period, the system evolves to a corner-localized state in a quadrupole configuration. The robustness of the second-order topological pump is also investigated by introducing different on-site disorder. Our Letter studies the topological properties of high-order topological phases from the dynamical transport picture using superconducting qubits, which would inspire further research on high-order topological phases.

DOI
10.1103/physrevlett.133.140402

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High-order topological phases of matter refer to the systems of n-dimensional bulk with the topology of m-th order, exhibiting (n-m)-dimensional boundary modes and can be characterized by topological pumping. Here, we experimentally demonstrate two types of second-order topological pumps, forming four 0-dimensional corner localized states on a 4×4 square lattice array of 16 superconducting qubits. The initial ground state of the system at half-filling, as a product of four identical entangled 4-qubit states, is prepared using an adiabatic scheme. During the pumping procedure, we adiabatically modulate the superlattice Bose-Hubbard Hamiltonian by precisely controlling both the hopping strengths and on-site potentials. At the half pumping period, the system evolves to a corner-localized state in a quadrupole configuration. The robustness of the second-order topological pump is also investigated by introducing different on-site disorder. Our Letter studies the topological properties of high-order topological phases from the dynamical transport picture using superconducting qubits, which would inspire further research on high-order topological phases.
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An extended Bose-Hubbard model (EBHM) with three- and four-body constraints can be feasible in cold atoms in an optical lattice. A rich phase structure including various symmetry-protected topological (SPT) phases is obtained numerically with suitable parameter settings and particle filling. The SPT phase is characterized by the Berry phase as a local topological order parameter and the structure of the entanglement spectrum (ES). Based on the presence of various topological phases, separated by gapless phase boundaries, the EBHM exhibits various bosonic topological pumps, which are constructed by connecting the different SPT phases without gap closing. The bulk topological pumps exhibit the plateau transitions characterized by many-body Chern numbers. For the system with boundary, the center of mass (CoM) under grand canonical ensemble elucidates the contributions of multiple edge states and reveals the topology of the system. We demonstrate that the interacting bosonic pumps obey the bulk-edge correspondence.
Topological insulators lie outside the standard Landau paradigm: Instead of being characterized by local order parameters and spontaneous symmetry breaking, their defining properties are encoded in the global structure of their quantum states and manifested as robust boundary states. Crystalline higher-order topological insulators can extend this principle by hosting localized corner modes in two and higher dimensions. Although these boundary modes can be detected spectroscopically through the local density of states, determining the underlying bulk topology, for example through nested Wilson loops, remains an outstanding experimental challenge. Here we use up to 728 qubits in a superconducting analogue-digital quantum simulator to realize and probe a hierarchy of one-, two-, and three-dimensional topological insulators governed by effective tight-binding Hamiltonians. By reconstructing complex propagators from real-space measurements, we obtain complementary boundary and bulk characterizations: local densities of states reveal localized boundary modes, whereas experimentally reconstructed band projectors yield bulk topological invariants, culminating in a three-dimensional octupole moment extracted through third nested Wilson loops. These results establish a route to realizing, characterizing, and manipulating topologically protected states in programmable three-dimensional quantum matter.
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Simulating higher-order topological materials in synthetic quantum matter is an active research frontier for its theoretical significance in fundamental physics and promising applications in quantum technologies. Here we experimentally implement two-dimensional (2D) momentum lattices with highly programmable ability using ultracold 87Rb atoms. Through precise control of experimental parameters, we simulate a 2D Su-Schrieffer-Heeger model with this technique, and observe the characteristic dynamics of corner and edge-bound states, where the corner state is identified as a higher-order topological bound state in the continuum. We further study the adiabatic preparation of the corner state by engineering evolutions with time-dependent Hamiltonians. We also demonstrate the higher-order topological phase transition by measuring both the bulk topological invariant and the topological corner state. Our new platform opens the avenue for exploring the exotic dynamics and topology in higher synthetic dimensions, making use of the rich degrees of freedom of cold atoms systems.