Journal
ADVANCES IN PHYSICS
Volume 64, Issue 2, Pages 139-226Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00018732.2015.1055918
Keywords
Floquet theory; effective Hamiltonian; Magnus expansion; high-frequency limit; quantum simulation; dynamical stabilization and localization; artificial gauge fields; topological insulators; spin systems
Categories
Funding
- AFOSR [FA9550-13-1-0039]
- ARO [W911NF1410540]
- NSF [DMR-1206410]
- BSF [2010318]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1206410] Funding Source: National Science Foundation
Ask authors/readers for more resources
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available