Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering
By Marin Bukov, Luca D'Alessio, A. Polkovnikov. 2014
1,193 citations recorded by the source corpus.
We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper–Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case, one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer–Wolff transformation extending the latter to driven systems.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/ef9b4b563a2956f933dfb22467287e4986c0cd7b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Colloquium: Nonthermal pathways to ultrafast control in quantum materials (2021, background): “Further reviews on Floquet engineering can be found in (Bukov et al., 2015; Oka and Kitamura, 2019; Rudner and Lindner, 2020).”
- A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems (2015, background): “Such periodically driven quantum systems exhibit rich and often unexpected behaviour [8].”
- Prethermalization and Thermalization in Isolated Quantum Systems (2018, background): “In general, they quickly reach a time-periodic state that can be identified as a Gibbs state corresponding to an effective Hamiltonian, before relaxing to the thermal (infinite-temperature [26, 27]) state in a timescale that is exponentially long in the frequency of the drive [28–33].”
- Topological photonics (2018, background): “However, due to the time-periodicity inherent to the system Ĥ(t+T )=Ĥ(t), this time-evolution operator can be factorized, leading to the more suggestive form (Bukov et al., 2015; Goldman and Dalibard, 2014; Kiss et al., 1994; Rahav et al., 2003)”