Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems

Abstract

We give a systematic review of the adiabatic theorem and the leading non-adiabatic corrections in periodically-driven (Floquet) systems. These corrections have a two-fold origin: (i) conventional ones originating from the gradually changing Floquet Hamiltonian and (ii) corrections originating from changing the micro-motion operator. These corrections conspire to give a Hall-type linear response for non-stroboscopic (time-averaged) observables allowing one to measure the Berry curvature and the Chern number related to the Floquet Hamiltonian, thus extending these concepts to periodically-driven many-body systems. The non-zero Floquet Chern number allows one to realize a Thouless energy pump, where one can adiabatically add energy to the system in discrete units of the driving frequency. We discuss the validity of Floquet Adiabatic Perturbation Theory (FAPT) using five different models covering linear and non-linear few and many-particle systems. We argue that in interacting systems, even in the stable high-frequency regimes, FAPT breaks down at ultra slow ramp rates due to avoided crossings of photon resonances, not captured by the inverse-frequency expansion, leading to a counter-intuitive stronger heating at slower ramp rates. Nevertheless, large windows in the ramp rate are shown to exist for which the physics of interacting driven systems is well captured by FAPT.

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• Reinforcement Learning in Different Phases of Quantum Control
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• Non-Hermitian Floquet Topological Matter -- A Review
• Floquet Engineering in Quantum Chains
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• Parametric instabilities in a 2D periodically-driven bosonic system: Beyond the weakly-interacting regime
• Spin polarization through Floquet resonances in a driven central spin model
• Half-integer quantized topological response in quasiperiodically driven quantum systems
• Topological Frequency Conversion in a Driven Dissipative Quantum Cavity
• Low-frequency phase diagram of irradiated graphene and periodically driven spin-1/2 $XY$ chain
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• Driven quantum many-body systems and out-of-equilibrium topology
• Topology and localization of a periodically driven Kitaev model
• Valley-selective Floquet Chern Flat Bands in Twisted Multilayer Graphene
• Amplified and tunable transverse and longitudinal spin-photon coupling in hybrid circuit-QED
• From non-equilibrium Green's functions to quantum master equations for the density matrix and out-of-time-order correlators: steady state and adiabatic dynamics
• Dispersion Suppressed Topological Thouless Pumping
• Adiabatic landscape and optimal paths in ergodic systems
• Thermodynamic Cost for Classical Counterdiabatic Driving
• Floquet resonances close to the adiabatic limit and the effect of dissipation
• Edge mode manipulation through commensurate multifrequency driving
• Error bounds for constrained dynamics in gapped quantum systems: Rigorous results and generalizations
• Counterdiabatic Driving for Periodically Driven Systems
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• Demonstrating Majorana non-Abelian properties using fast adiabatic charge-transfer
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