Quantum dynamical characterization and simulation of topological phases with high-order band inversion surfaces

Abstract

How to characterize topological quantum phases is a fundamental issue in the broad field of topological matter. From a dimension reduction approach, we propose the concept of high-order band inversion surfaces (BISs) which enable the optimal schemes to characterize equilibrium topological phases by far-from-equilibrium quantum dynamics, and further report the experimental simulation. We show that characterization of a d-dimensional (dD) topological phase can be reduced to lower-dimensional topological invariants in the high-order BISs, of which the nth-order BIS is a (d-n)D interface in momentum space. In quenching the system from trivial phase to topological regime, we unveil a high-order dynamical bulk-surface correspondence that the quantum dynamics exhibits nontrivial topological pattern in arbitrary nth-order BISs, which universally corresponds to and so characterizes the equilibrium topological phase of the post-quench Hamiltonian. This high-order dynamical bulk-surface correspondence provides new and optimal dynamical schemes with fundamental advantages to simulate and detect topological states, in which through the highest-order BISs that are of zero dimension, the detection of topological phase relies on only minimal measurements. We experimentally build up a quantum simulator with spin qubits to investigate a 3D chiral topological insulator through emulating each momentum one by one and measure the high-order dynamical bulk-surface correspondence, with the advantages of topological characterization via highest-order BISs being demonstrated.

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Cited by in corpus (22)

• Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Simulation of Higher-Order Topological Phases and Related Topological Phase Transitions in a Superconducting Qubit
• Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces
• Topological holographic quench dynamics in a synthetic dimension
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• Unified characterization for higher-order topological phase transitions
• Universal topological quench dynamics: Altland-Zirnbauer tenfold classes
• Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation
• Unconventional Floquet topological phases from quantum engineering of band inversion surfaces
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
• Generic theory of characterizing topological phases under quantum slow dynamics
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Topological spin-orbit-coupled fermions beyond rotating wave approximation
• Unconventional hybrid-order topological insulators
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Dynamical characterization of topological phases beyond the minimal models
• Characterizing Floquet topological phases by quench dynamics: A multiple-subsystem approach
• Generic reduction theory for Fermi sea topology in metallic systems
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• Loop unitary and phase band topological invariant in generic multi-band Chern insulators
• Observation of symmetry-protected selection rules in periodically driven quantum systems