Quasi-periodically driven quantum systems

Abstract

Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well understood. Here, we provide a critical review of the theoretical framework developed for quasi-periodically driven quantum systems. Although the theoretical footing is still under development, we argue that quasi-periodically driven quantum systems can be treated with generalizations of Floquet theory in suitable parameter regimes. Moreover, we provide a generalization of the Floquet-Magnus expansion and argue that quasi-periodic driving offers a promising route for quantum simulations.

References in corpus (8)

• The Magnus expansion and some of its applications
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Dynamical control of matter-wave tunneling in periodic potentials
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Quasiperiodically driven ratchets for cold atoms

Cited by in corpus (46)

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• Steady Floquet-Andreev States Probed by Tunnelling Spectroscopy
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• Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit
• Nonadiabatic Topological Energy Pumps with Quasiperiodic Driving
• Floquet Time Spirals and Stable Discrete Time Quasi-Crystals in Quasi-Periodically Driven Quantum Many-Body Systems
• Half-integer quantized topological response in quasiperiodically driven quantum systems
• Geometric aspects of nonlinear and nonequilibrium phenomena
• Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems
• Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives
• Many-Body Localization with Quasiperiodic Driving
• A Floquet perturbation theory for periodically driven weakly-interacting fermions
• Dynamical relaxation of correlators in periodically driven integrable quantum systems
• Out-of-Time-Order correlators in driven conformal field theories
• Dynamical localization and slow dynamics in quasiperiodically-driven quantum systems
• Boosting the Quantum State of a Cavity with Floquet Driving
• Dynamical localization and slow thermalization in a class of disorder-free periodically driven one-dimensional interacting systems
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Localization persisting under aperiodic driving
• Interacting topological frequency converter
• On the validity of many-mode Floquet theory with commensurate frequencies
• Real-space topological invariant for time-quasiperiodic Majoranas
• Hilbert-Space Ergodicity in Driven Quantum Systems: Obstructions and Designs
• Suppression of inter-band heating for random driving
• Scalable quantum control and non-abelian anyon creation in the Kitaev honeycomb model
• Coupled Layer Construction for Synthetic Hall Effects in Driven Systems
• Prethermalization in the PXP Model under Continuous Quasiperiodic Driving
• On Howland time-independent formulation of CP-divisible quantum evolutions
• Fibered rotation vector and hypoellipticity for quasiperiodic cocycles in compact Lie groups
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• From time crystals to time quasicrystals: Exploring quasiperiodic phases in transverse field Ising chains
• Topological frequency conversion in rhombohedral multilayer graphene
• Quantum control without quantum states
• Absence of disordered Thouless pumps at finite frequency
• Stable time rondeau crystals in dissipative many-body systems
• Instability Zones in the Dynamics of a Quantum Mechanical Quasiperiodic Parametric Oscillator
• Nonlinear dynamics of superpostion of wavepackets
• openMMF: a library for multimode driven quantum systems
• Emergence of prethermal time quasicrystalline order in a quasiperiodically driven non-interacting spin chain
• Topological energy pumping in a quasi-periodically driven four-level system
• Effective Hamiltonians for almost-periodically driven quantum systems
• Detecting the $\pi$-axiverse through parametric resonance
• A strong-driving toolkit for topological Floquet energy pumps with superconducting circuits