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 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 …

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 …

Driving a quantum system periodically in time can profoundly alter its long-time dynamics
and trigger topological order. Such schemes are particularly promising for generating …

Gauge fields are central in our modern understanding of physics at all scales. At the highest
energy scales known, the microscopic universe is governed by particles interacting with …

This article reviews recent theoretical and experimental advances in the fundamental
understanding and active control of quantum fluids of light in nonlinear optical systems. In …

Quantum computers, though not yet available on the market, will revolutionize the future of
information processing. Quantum computers for special purposes like quantum simulators …

We describe a simple technique for generating a cold-atom lattice pierced by a uniform
magnetic field. Our method is to extend a one-dimensional optical lattice into the …

Originally, the Hubbard model was derived for describing the behavior of strongly correlated
electrons in solids. However, for over a decade now, variations of it have also routinely been …

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 …