Half-integer quantized topological response in quasiperiodically driven quantum systems

Abstract

A spin strongly driven by two harmonic incommensurate drives can pump energy from one drive to the other at a quantized average rate, in close analogy with the quantum Hall effect. The pumping rate is a non-zero integer in the topological regime, while the trivial regime does not pump. The dynamical transition between the regimes is sharp in the zero-frequency limit and is characterized by a Dirac point in a synthetic band structure. We show that the pumping rate is {\em half-integer} quantized at the transition and present universal Kibble-Zurek scaling functions for energy transfer processes. Our results adapt ideas from quantum phase transitions, quantum information and topological band theory to non-equilibrium dynamics, and identify qubit experiments to observe the universal linear and non-linear response of a Dirac point in synthetic dimensions.

10 pages, 8 figures

References in corpus (67)

• Topological Insulators
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Colloquium: Topological Band Theory
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Quantum computing with trapped ions
• Spin qubits in graphene quantum dots
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Floquet Engineering of Quantum Materials
• On the phase structure of driven quantum systems
• Quantum information processing with superconducting circuits: a review
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Dynamics of a Quantum Phase Transition
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Natural and artificial atoms for quantum computation
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
• Universal adiabatic dynamics across a quantum critical point
• Floquet topological insulators
• Prospects for Spin-Based Quantum Computing
• Topological quantum matter in synthetic dimensions
• Long-lived qubit memory using atomic ions
• Dynamical phase transition in the open Dicke model
• Periodic Table for Floquet Topological Insulators
• Dynamical Critical Phenomena in Driven-Dissipative Systems
• Single-qubit quantum memory exceeding $10$-minute coherence time
• Equilibration and Order in Quantum Floquet Matter
• Floquet Fractional Chern Insulator in Doped Graphene
• Cooperative non-equilibrium phase transition in a dilute Rydberg ensemble
• The Kibble-Zurek Problem: Universality and the Scaling Limit
• Classification of topological phases in periodically driven interacting systems
• Effective Theory of Floquet Topological Transitions
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Merging of Dirac points and Floquet topological transitions in AC driven graphene
• 1D Many-body localized Floquet systems II: Symmetry-Broken phases
• Critical dynamical properties of a first-order dissipative phase transition
• Universal non-equilibrium properties of dissipative Rydberg gases
• Modulated Floquet Topological Insulators
• Topological frequency conversion in strongly driven quantum systems
• Observation of a Dissipation-Induced Classical to Quantum Transition
• Floquet second-order topological insulators from nonsymmorphic space-time symmetries
• Non-equilibrium dynamic critical scaling of the quantum Ising chain
• Dynamical Singularities of Floquet Higher-Order Topological Insulators
• Beyond the Quantum Adiabatic Approximation: Adiabatic Perturbation Theory
• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Driven Markovian Quantum Criticality
• Abelian Floquet symmetry-protected topological phases in one dimension
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Counter-propagating edge modes and topological phases of a kicked quantum Hall system
• Universal nonequilibrium quantum dynamics in imaginary time
• Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin Chains
• Kibble-Zurek mechanism and infinitely slow annealing through critical points
• Topological Floquet-Thouless energy pump
• Topological classification of quasi-periodically driven quantum systems
• Materials design from non-equilibrium steady states: driven graphene as a tunable semiconductor with topological properties
• Quantized magnetization density in periodically driven systems
• Interaction stabilized steady states in the driven O(N) model
• Topologically protected braiding in a single wire using Floquet Majorana modes
• Quasi-periodically driven quantum systems
• Time-quasiperiodic topological superconductors with Majorana Multiplexing
• Topological energy conversion through bulk or boundary of driven systems
• Phase Transitions and Scaling in Systems Far From Equilibrium
• Topological Frequency Conversion in a Driven Dissipative Quantum Cavity
• Tuning universality far from equilibrium
• Setting Boundaries with Memory: Generation of Topological Boundary States in Floquet-Induced Synthetic Crystals

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• Energy dynamics, heat production and heat-work conversion with qubits: towards the development of quantum machines
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• Nonadiabatic Topological Energy Pumps with Quasiperiodic Driving
• Floquet-Engineered Topological Flat Bands in Irradiated Twisted Bilayer Graphene
• Thermalization and Prethermalization in Periodically Kicked Quantum Spin Chains
• Many-Body Localization with Quasiperiodic Driving
• Edge mode manipulation through commensurate multifrequency driving
• Heating Rates under Fast Periodic Driving beyond Linear Response
• Boosting the Quantum State of a Cavity with Floquet Driving
• Universal nonadiabatic energy pumping in a quasiperiodically driven extended system
• Unified Light-Matter Floquet Theory and its Application to Quantum Communication
• Superfluid Vortices in Four Spatial Dimensions
• Real-space topological invariant for time-quasiperiodic Majoranas
• Energy polarization and energy pumping in Rice-Mele chains
• Nonequilibrium Critical Dynamics with Emergent Supersymmetry
• Prethermalization by Random Multipolar Driving on a 78-Qubit Superconducting Processor
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Coupled Layer Construction for Synthetic Hall Effects in Driven Systems
• Dissipative frequency converter: from Lindblad dynamics to non-Hermitian topology
• Topological frequency conversion in rhombohedral multilayer graphene
• Topological Burning Glass Effect
• Curved vortex surfaces in four-dimensional superfluids: II. Equal-frequency double rotations
• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• Absence of disordered Thouless pumps at finite frequency
• A strong-driving toolkit for topological Floquet energy pumps with superconducting circuits
• Topological dynamics of adiabatic cat states
• Topological energy pumping in a quasi-periodically driven four-level system
• Non-abelian Geometric Quantum Energy Pump
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking