There have been significant recent advances in realizing band structures with geometrical
and topological features in experiments on cold atomic gases. This review summarizes …

Time-periodic forcing in the form of coherent radiation is a standard tool for the coherent
manipulation of small quantum systems like single atoms. In the last years, periodic driving …

We derive a systematic high-frequency expansion for the effective Hamiltonian and the
micromotion operator of periodically driven quantum systems. Our approach is based on the …

Artificial gauge fields are currently realized in a wide range of physical settings. This
includes solid-state devices but also engineered systems, such as photonic crystals …

Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic
quantum phases. While driven many-body systems are generically expected to absorb …

A primer on the Floquet theory of periodically time-dependent quantum systems is provided,
and it is shown how to apply this framework for computing the quasienergy band structure …

The topology of two-dimensional materials traditionally manifests itself through the
quantization of the Hall conductance, which is revealed in transport measurements …

We present a platform for the simulation of quantum magnetism with full control of
interactions between pairs of spins at arbitrary distances in 1D and 2D lattices. In our …

We review recent work on low-frequency Floquet engineering and its application to quantum
materials driven by light, focusing on van der Waals systems hosting Moiré superlattices …

Periodic driving of optical lattices has enabled the creation of novel band structures not
realizable in static lattice systems, such as topological bands for neutral particles. However …