Topological energy pumping in a quasi-periodically driven four-level system
arXiv:2509.06043 · doi:10.1103/prg5-3srn
Abstract
We investigate a quasi-periodically driven four-level system that serves as a temporal analog of topological phenomena found in four-band models with intertwined spin and orbital degrees of freedom. Under a two-tone drive in the strong-driving regime, the system realizes a two-dimensional synthetic Floquet lattice, thus facilitating the realization of topological energy pumping. For a temporal quantum spin Hall insulator, we find that the rates of emission and absorption of energy between the two drives are not exactly opposite for a given band. However, when contributions from two chiral symmetric partner bands are added, they become exactly opposite. This quantized rate of energy exchange is a direct consequence of propagating edge modes in the real-space model, which we further characterize by computing the spin-Chern number. Interestingly, our analysis yields zero rate of exchange of energy between the drives for a temporal higher-order topological insulator, suggesting the presence of localized corner modes that we characterize by the mid-gap Wannier spectra. {Our findings uncover the role of chiral, particle-hole and time reversal symmetries on the energy dynamics in temporal quantum spin Hall and higher-order topological insulators.} Finally, we demonstrate that the perfect (imperfect) nature of the fidelity during the time-evolution of the system serves as a characteristic signature of a topological (trivial) phase.
17 pages, 7 figures
References in corpus (123)
- Topological Insulators
- Topological insulators and superconductors
- Quantum Spin Hall Effect in Graphene
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Topological Order and the Quantum Spin Hall Effect
- Topological Insulators in Three Dimensions
- Topological Insulators with Inversion Symmetry
- Photonic Floquet Topological Insulators
- Topological invariants of time-reversal-invariant band structures
- Experimental realisation of the topological Haldane model
- Quantum Spin Hall Effect
- Topological Crystalline Insulators
- Quantized Electric Multipole Insulators
- Floquet Topological Insulator in Semiconductor Quantum Wells
- Higher-Order Topological Insulators
- Photovoltaic Hall effect in graphene
- Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
- Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
- Topological Acoustics
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- Observation of Floquet-Bloch states on the surface of a topological insulator
- Topological characterization of periodically-driven quantum systems
- Acoustic topological insulator and robust one-way sound transport
- Atomic quantum gases in periodically driven optical lattices
- -dimensional edge states of rotation symmetry protected topological states
- Reflection symmetric second-order topological insulators and superconductors
- Floquet Engineering of Quantum Materials
- Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
- Floquet Time Crystals
- Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
- On the phase structure of driven quantum systems
- Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
- Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
- A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
- Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
- Discrete time crystals: rigidity, criticality, and realizations
- Direct observation of corner states in second-order topological photonic crystal slabs
- Classical higher-order topological insulators
- Higher-order topological insulators and superconductors protected by inversion symmetry
- Second-order topological insulators and superconductors with an order-two crystalline symmetry
- Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon
- A universal qudit quantum processor with trapped ions
- Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe (X=Mo,W)
- Higher-order bulk-boundary correspondence for topological crystalline phases
- Higher-order topological corner states induced by gain and loss
- Quantized Response and Topology of Insulators with Inversion Symmetry
- Effective Theory of Floquet Topological Transitions
- Higher Order Topological Phases: A General Principle of Construction
- A theory of many-body localization in periodically driven systems
- Colloquium: Quantum and Classical Discrete Time Crystals
- An anomalous higher-order topological insulator
- Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms
- Minimal model for higher-order topological insulators and phosphorene
- Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
- Material design with the van der Waals stacking of bismuth-halide chains realizing a higher-order topological insulator
- Demonstration of a quantized acoustic octupole topological insulator
- Topological Floquet Spectrum in Three Dimensions via a Two-Photon Resonance
- Higher-order topological insulators in amorphous solids
- Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms
- Clean Floquet Time Crystals: Models and Realizations in Cold Atoms
- Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
- Native qudit entanglement in a trapped ion quantum processor
- A Floquet Model for the Many-Body Localization Transition
- Counter-propagating edge modes and topological phases of a kicked quantum Hall system
- Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin Chains
- Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics
- Evidence for Higher order topology in Bi and BiSb
- Antiunitary symmetry protected higher order topological phases
- Topological classification of quasi-periodically driven quantum systems
- Floquet generation of Second Order Topological Superconductor
- Floquet higher order topological insulator in a periodically driven bipartite lattice
- Random multipolar driving: tunably slow heating through spectral engineering
- Aperiodically driven integrable systems and their emergent steady states
- Higher-order topological band structures
- Dynamical synchronization transition in interacting electron systems
- Quasi-periodically driven quantum systems
- Hierarchy of higher-order topological superconductors in three dimensions
- Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit
- Simple model for second-order topological insulators and loop-nodal semimetals in Transition Metal Dichalcogenides XTe (X=Mo,W)
- Performing SU() operations and rudimentary algorithms in a superconducting transmon qudit for and
- Floquet Time Spirals and Stable Discrete Time Quasi-Crystals in Quasi-Periodically Driven Quantum Many-Body Systems
- Nonadiabatic Topological Energy Pumps with Quasiperiodic Driving
- Time-quasiperiodic topological superconductors with Majorana Multiplexing
- Large Spin Hall Effect in an Amorphous Binary Alloy
- Half-integer quantized topological response in quasiperiodically driven quantum systems
- Higher-order topological phases in crystalline and non-crystalline systems: a review
- Suppressing dissipation in a Floquet-Hubbard system
- Floquet Second Order Topological Superconductor based on Unconventional Pairing
- Quantized topological energy pumping and Weyl points in Floquet synthetic dimensions with a driven-dissipative photonic molecule
- Quasi-Floquet prethermalization in a disordered dipolar spin ensemble in diamond
- Time reflection and refraction in synthetic frequency dimension
- Topological Floquet engineering using two frequencies in two dimensions
- Qudit entanglers using quantum optimal control
- An eternal discrete time crystal beating the Heisenberg limit
- Many-Body Localization with Quasiperiodic Driving
- Topological characterization and stability of Floquet Majorana modes in Rashba nanowire
- Qudit Dynamical Decoupling on a Superconducting Quantum Processor
- Dynamical construction of Quadrupolar and Octupolar topological superconductors
- Experimental Realization of Discrete Time Quasi-Crystals
- Generation of higher-order topological insulators using periodic driving
- Topological frequency conversion in Weyl semimetals
- Engineering anomalous Floquet Majorana modes and their time evolution in helical Shiba chain
- Eight fold quantum Hall phases in a time reversal symmetry broken tight binding model
- Universal nonadiabatic energy pumping in a quasiperiodically driven extended system
- Localization persisting under aperiodic driving
- Interacting topological frequency converter
- Real-space topological invariant for time-quasiperiodic Majoranas
- Experimental observation of a time rondeau crystal: Temporal Disorder in Spatiotemporal Order
- Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation
- Self-similar phase diagram of the Fibonacci-driven quantum Ising model
- Prethermalization in aperiodically driven classical spin systems
- Counterdiabatic Route to Entanglement Steering and Dynamical Freezing in the Floquet Lipkin-Meshkov-Glick Model
- Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics
- Controllable Floquet edge modes in a multi-frequency driving system
- Energy Transfer in Random-Matrix ensembles of Floquet Hamiltonians
- Prethermalization in the PXP Model under Continuous Quasiperiodic Driving
- Coupled Layer Construction for Synthetic Hall Effects in Driven Systems
- Topological frequency conversion in rhombohedral multilayer graphene
- Stable time rondeau crystals in dissipative many-body systems
- Statistical prethermalization in randomly kicked many-body classical rotor system
- Unitary Transformations using Robust Optimal Control on a Cold Atom Qudit
- Quasi-Discrete Time Crystals in the quasiperiodically driven Lipkin-Meshkov-Glick model
- Extended Haldane model -- a modern gateway to topological insulators