Periodic driving of quantum systems is attracting interest since we can use it to realize new states of matter with exotic properties. This concept, known as Floquet engineering, has been widely used in cold atoms [1] and recently in solid-state systems [2]. In this talk, I plan to explain Floquet engineering basics using simple examples such a 2D and 3D Dirac electrons in circularly polarized laser fields [2]. Then, to develop a more in-depth and intuitive understanding of Floquet states, I will explain an example of a dynamical Landau quantization realized in oscillating magnetic fields.

1. A. Eckardt, Rev. Mod. Phys. 89, 011004 (2017).
2. T. Oka, S. Kitamura, Annual Reviews of CMP, 10:387 (2019).
3. T. Oka, L. Bucciantini, Phys. Rev. B 94, 155133 (2016).