Nonadiabatic Topological Energy Pumps with Quasiperiodic Driving

Abstract

We derive a topological classification of the steady states of $d$-dimensional lattice models driven by $D$ incommensurate tones. Mapping to a unifying $(d+D)$-dimensional localized model in frequency space reveals anomalous localized topological phases (ALTPs) with no static analog. While the formal classification is determined by $d+D$, the observable signatures of each ALTP depend on the spatial dimension $d$. For each $d$, with $d+D=3$, we identify a quantized circulating current, and corresponding topological edge states. The edge states for a driven wire ($d=1$) function as a quantized, nonadiabatic energy pump between the drives. We design concrete models of quasiperiodically driven qubits and wires that achieve ALTPs of several topological classes. Our results provide a route to experimentally access higher dimensional ALTPs in driven low-dimensional systems.

arXiv comment6 pages, 3 figures + 13 pages, 5 figures

References in corpus (52)

• Many-Body Physics with Ultracold Gases
• Topological Photonics
• The nitrogen-vacancy colour centre in diamond
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Periodic table for topological insulators and superconductors
• Localization of interacting fermions at high temperature
• Many-body localization, thermalization, and entanglement
• Superconducting Qubits: Current State of Play
• Topological characterization of periodically-driven quantum systems
• Topological States and Adiabatic Pumping in Quasicrystals
• Shortcuts to adiabaticity: concepts, methods, and applications
• Topological Defects and Gapless Modes in Insulators and Superconductors
• High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Topological Thouless Pumping of Ultracold Fermions
• An Adiabatic Quantum Electron Pump
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Spectral signatures of many-body localization with interacting photons
• Experimental observation of the Anderson transition with atomic matter waves
• Localization protected quantum order
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Topological quantum matter in synthetic dimensions
• Periodic Table for Floquet Topological Insulators
• Topological singularities and the general classification of Floquet-Bloch systems
• Minimizing irreversible losses in quantum systems by local counter-diabatic driving
• The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Higher Order Decompositions of Ordered Operator Exponentials
• Topological frequency conversion in strongly driven quantum systems
• Quasiperiodically driven ratchets for cold atoms
• Time Quasi-periodic unbounded perturbations of Schrödinger operators and KAM methods
• Hopf Insulators and Their Topologically Protected Surface States
• Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin Chains
• Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems
• Anomalous Floquet Insulators
• Topological Floquet-Thouless energy pump
• Topological classification of quasi-periodically driven quantum systems
• Quantized magnetization density in periodically driven systems
• Hopf characterization of two-dimensional Floquet topological insulators
• Aperiodically driven integrable systems and their emergent steady states
• Quasi-periodically driven quantum systems
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit
• Time-quasiperiodic topological superconductors with Majorana Multiplexing
• Floquet Time Spirals and Stable Discrete Time Quasi-Crystals in Quasi-Periodically Driven Quantum Many-Body Systems
• Topological energy conversion through bulk or boundary of driven systems
• Half-integer quantized topological response in quasiperiodically driven quantum systems
• Topological Frequency Conversion in a Driven Dissipative Quantum Cavity
• Dynamics of quasiperiodically driven spin systems
• Topologically quantized current in quasiperiodic Thouless pumps
• Steady states of a quasiperiodically driven integrable system
• Quantum frequency locking and down-conversion in a driven cavity-qubit system
• Asymptotic theory of quasiperiodically driven quantum systems

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• 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
• Localization persisting under aperiodic driving
• Unified Light-Matter Floquet Theory and its Application to Quantum Communication
• Floquet band engineering with Bloch oscillations
• Real-space topological invariant for time-quasiperiodic Majoranas
• Self-similar phase diagram of the Fibonacci-driven quantum Ising model
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• Quantized topological phases beyond square lattices in Floquet synthetic dimensions
• Coupled Layer Construction for Synthetic Hall Effects in Driven Systems
• Topology of ultra-localized insulators and superconductors
• Topological frequency conversion in rhombohedral multilayer graphene
• Dissipative frequency converter: from Lindblad dynamics to non-Hermitian topology
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• Autonomous Stabilization of Floquet States Using Static Dissipation
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• Universal quantum control over Majorana zero modes
• Absence of disordered Thouless pumps at finite frequency
• Nonadiabatic braiding of Majorana modes
• Recent progress on disorder-induced topological phases
• A strong-driving toolkit for topological Floquet energy pumps with superconducting circuits
• Topological energy pumping in a quasi-periodically driven four-level system
• Topological dynamics of adiabatic cat states
• Topological anomalous Floquet photon pump