Floquet Perturbation Theory: Formalism and Application to Low-Frequency Limit

Abstract

We develop a low-frequency perturbation theory in the extended Floquet Hilbert space of a periodically driven quantum systems, which puts the high- and low-frequency approximations to the Floquet theory on the same footing. It captures adiabatic perturbation theories recently discussed in the literature as well as diabatic deviation due to Floquet resonances. For illustration, we apply our Floquet perturbation theory to a driven two-level system as in the Schwinger-Rabi and the Landau-Zener-Stückelberg-Majorana models. We reproduce some known expressions for transition probabilities in a simple and systematic way and clarify and extend their regime of applicability. We then apply the theory to a periodically-driven system of fermions on the lattice and obtain the spectral properties and the low-frequency dynamics of the system.

v2: 28 single-column pages, 5 figures; various typos fixed; some notation and connection to other perturbation schemes clarified; new, more descriptive title and abstract. Published version

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• Measurement-only quantum computation with Majorana corner modes
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• A flow equation approach to periodically driven quantum systems
• Effective Floquet Hamiltonian in the low-frequency regime
• Parametric resonance of Josephson plasma waves: A theory for optically amplified interlayer superconductivity in YBa${}_2$Cu${}_3$O${}_{6+x}$
• Effective Floquet Hamiltonians for periodically-driven twisted bilayer graphene
• Floquet engineering of interlayer couplings: Tuning the magic angle of twisted bilayer graphene at the exit of a waveguide
• Floquet-engineering topological transitions in a twisted transition metal dichalcogenide homobilayer
• Floquet engineering of twisted double bilayer graphene
• Linear Response Theory and Optical Conductivity of Floquet Topological Insulators
• Thermalization and Prethermalization in Periodically Kicked Quantum Spin Chains
• Prethermalization and Thermalization in Periodically-Driven Many-Body Systems away from the High-Frequency Limit
• Floquet-Bloch Oscillations and Intraband Zener Tunneling in an Oblique Spacetime Crystal
• A Floquet perturbation theory for periodically driven weakly-interacting fermions
• Chiral 1D Floquet topological insulators beyond rotating wave approximation
• Ultrafast Control of Spin Interactions in Honeycomb Antiferromagnetic Insulators
• Generation of higher-order topological insulators using periodic driving
• Floquet spectrum for anisotropic and tilted Dirac materials under linearly polarized light at all field intensities
• Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene
• Floquet Topological Semimetal with Nodal Helix
• Quantum computing Floquet energy spectra
• Josephson-Current Signatures of Unpaired Floquet Majorana Bound States
• Transport signatures of symmetry protection in 1D Floquet topological insulators
• Pymablock: an algorithm and a package for quasi-degenerate perturbation theory
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• Real-time simulation of light-driven spin chains on quantum computers
• Dynamic renormalization group theory for open Floquet systems
• Floquet Analysis of Frequency Collisions
• Estimating heating times in periodically driven quantum many-body systems via avoided crossing spectroscopy
• Floquet Engineering of Lie Algebraic Quantum Systems
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• Defining a well-ordered Floquet basis by the average energy
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• Ultrafast pseudomagnetic fields from electron-nuclear quantum geometry
• Direct driving of electronic and phononic degrees of freedom in a honeycomb bilayer with infrared light
• Design algorithms of driving-induced nonreciprocal components
• Low-frequency and Moiré Floquet engineering: a review
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• Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology
• Floquet Schrieffer-Wolff transform based on Sylvester equations
• Multiple tunable real-space degeneracies in graphene irradiated by twisted light
• Algebraic law of local correlations in a driven Rydberg atomic system
• Extended degenerate perturbation theory for the Floquet-Hilbert space
• Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene
• Localization and topological signatures under periodic twisting