Characterizing the transition from topology to chaos in a kicked quantum system

Abstract

This work theoretically investigates the transition from topology to chaos in a periodically driven system consisting of a quantum top coupled to a spin-1/2 particle. The system is driven by two alternating interaction kicks per period. For small kick strengths, localized topologically protected bound states exist, and as the kick strengths increase, these states proliferate. However, at large kick strengths they gradually delocalize in stages, eventually becoming random orthonormal vectors as chaos emerges. We identify the delocalization of the bound states as a finite size effect where their proliferation leads to their eventual overlap. This insight allows us to make analytic predictions for the onset and full emergence of chaos which are supported by numerical results of the quasi-energy level spacing ratio and Rényi entropy. A dynamical probe is also proposed to distinguish chaotic from regular behavior.

arXiv comment11 pages, 6 figures

References in corpus (52)

• Fault-tolerant quantum computation by anyons
• Topological Photonics
• Topological Photonics
• Photonic Floquet Topological Insulators
• Chaos and Quantum Thermalization
• New directions in the pursuit of Majorana fermions in solid state systems
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Light-induced gauge fields for ultracold atoms
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Floquet Engineering of Quantum Materials
• Topological Bands for Ultracold Atoms
• Electron spin decoherence in quantum dots due to interaction with nuclei
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Riemannian symmetric superspaces and their origin in random matrix theory
• Equilibrium states of generic quantum systems subject to periodic driving
• The approach to thermal equilibrium in quantized chaotic systems
• Long-time behavior of periodically driven isolated interacting lattice systems
• Observation of the topological soliton state in the Su-Schrieffer-Heeger model
• Exponentially slow heating in periodically driven many-body systems
• Topological quantum matter in synthetic dimensions
• Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems
• Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
• Quantum simulation of an extra dimension
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
• Electron spin evolution induced by interaction with nuclei in a quantum dot
• Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
• Tailoring quantum gases by Floquet engineering
• Topological characterizations of an extended Su-Schrieffer-Heeger model
• Symmetry classes of disordered fermions
• Exact dynamics in the inhomogeneous central-spin model
• Time Averaged Quantum Dynamics and the Validity of the Effective Hamiltonian Model
• Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
• AIII and BDI Topological Systems at Strong Disorder
• Phase Space Crystals: A New Way to Create a Quasienergy Band Structure
• Coherent control of quantum topological states of light in Fock-state lattices
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Dynamics and decoherence in the central spin model using exact methods
• Population dynamics in Floquet realisation of Harper-Hofstadter Hamiltonian
• Anderson localization and Mott insulator phase in the time domain
• Quantum Rydberg Central Spin Model
• Anderson localization of a Rydberg electron along a classical orbit
• Optical Superradiance from Nuclear Spin Environment of Single Photon Emitters
• Synthetic Dimensions
• Quantum simulation of the central spin model with a Rydberg atom and polar molecules in optical tweezers
• Suppression of Heating by Multi-color Driving Protocols in Floquet Engineered Strongly Correlated Systems
• Many topological regions on the Bloch sphere of the spin-1/2 double kicked top