Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the
experimental investigation of ultracold gases made of highly magnetic atoms has …

Non-equilibrium topological phenomena can be induced in quantum many-body systems
using time-periodic fields (for example, by laser or microwave illumination). This Review …

Thouless pumping provides one of the simplest manifestations of topology in quantum
systems and has attracted a lot of recent interest, both theoretically and experimentally …

Over the past twenty-five years, mathematical concepts associated with geometric phases
have come to occupy a central place in our modern understanding of the physics of …

While Hermiticity lies at the heart of quantum mechanics, recent experimental advances in
controlling dissipation have brought about unprecedented flexibility in engineering non …

Topological photonics seeks to control the behaviour of the light through the design of
protected topological modes in photonic structures. While this approach originated from …

Floquet engineering, the control of quantum systems using periodic driving, is an old
concept in condensed matter physics dating back to ideas such as the inverse Faraday …

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

We extend the theory of dipole moments in crystalline insulators to higher multipole
moments. As first formulated in Benalcazar et al.[Science 357, 61 (2017) SCIEAS 0036-8075 …

Symmetry-protected topological (SPT) phases are many-body quantum states that are
topologically nontrivial as long as the relevant symmetries are unbroken. In this work we …