Controllable Floquet edge modes in a multi-frequency driving system

Abstract

A driven quantum system has been recently studied in the context of nonequilibrium phase transitions and their responses. In particular, for a periodically driven system, its dynamics are described in terms of the multi-dimensional Floquet lattice with a lattice size depending on number of driving frequencies and their rational or irrational ratio. So far, for a multi-frequency driving system, the energy pumping between the sources of frequencies has been widely discussed as a signature of topologically nontrivial Floquet bands. However, the unique edge modes emerging in the Floquet lattice has not been explored yet. Here, we discuss how the edge modes in the Floquet lattice are controlled and result in the localization at particular frequencies, when multiple frequencies are present and their magnitudes are commensurate values. First, we construct the minimal model to exemplify our argument, focusing on a two-level system with two driving frequencies. For strong frequency limit, one can describe the system as a quasi-one dimensional Floquet lattice where the effective hopping between the neighboring sites depends on the relative magnitudes of potential for two frequency modes. With multiple driving modes, there always exist the non-trivial Floquet lattice boundaries via controlling the frequencies and this gives rise to the states that are mostly localized at such Floquet lattice boundaries, i.e. particular frequencies. We suggest the time-dependent Creutz ladder model as a realization of our theoretical Hamiltonian and show the emergence of controllable Floquet edge modes.

References in corpus (25)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological characterization of periodically-driven quantum systems
• Atomic quantum gases in periodically driven optical lattices
• Topological States and Adiabatic Pumping in Quasicrystals
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Topological Thouless Pumping of Ultracold Fermions
• An Adiabatic Quantum Electron Pump
• Floquet scattering theory of quantum pumps
• Topological Polaritons
• End states, ladder compounds, and domain wall fermions
• Dissipative Floquet Topological Systems
• Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving
• Topological frequency conversion in strongly driven quantum systems
• Dynamical synchronization transition in interacting electron systems
• Nonadiabatic Topological Energy Pumps with Quasiperiodic Driving
• Quasiperiodic Floquet-Thouless energy pump
• Many-Body Localization with Quasiperiodic Driving
• Universal nonadiabatic energy pumping in a quasiperiodically driven extended system

Cited by in corpus (4)

• Stability of time-periodic $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonians with different periodicities
• Adiabatic modulation of driving protocols in periodically driven quantum systems
• Topological energy pumping in a quasi-periodically driven four-level system
• Distinct topological excitonic insulators characterized by quantum geometry