Realization of a fractional quantum Hall state with ultracold atoms.

Strongly interacting topological matter exhibits fundamentally new phenomena with potential applications in quantum information technology. Emblematic instances are fractional quantum Hall (FQH) states, in which the interplay of a magnetic field and strong interactions gives rise to fractionally charged quasi-particles, long-ranged entanglement and anyonic exchange statistics. Progress in engineering synthetic magnetic fields has raised the hope to create these exotic states in controlled quantum systems.

Quantum critical behaviour at the many-body localization transition.

Phase transitions are driven by collective fluctuations of a system's constituents that emerge at a critical point. This mechanism has been extensively explored for classical and quantum systems in equilibrium, whose critical behaviour is described by the general theory of phase transitions. Recently, however, fundamentally distinct phase transitions have been discovered for out-of-equilibrium quantum systems, which can exhibit critical behaviour that defies this description and is not well understood.

Probing entanglement in a many-body-localized system.

An interacting quantum system that is subject to disorder may cease to thermalize owing to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to understanding this phenomenon lies in the system's entanglement, which is experimentally challenging to measure. We realize such a many-body-localized system in a disordered Bose-Hubbard chain and characterize its entanglement properties through particle fluctuations and correlations.

Coupling two order parameters in a quantum gas.

Controlling matter to simultaneously support coupled properties is of fundamental and technological importance (for example, in multiferroics or high-temperature superconductors). However, determining the microscopic mechanisms responsible for the simultaneous presence of different orders is difficult, making it hard to predict material phenomenology or modify properties. Here, using a quantum gas to engineer an adjustable interaction at the microscopic level, we demonstrate scenarios of competition, coexistence and mutual enhancement of two orders.

Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas.

Higgs and Goldstone modes are collective excitations of the amplitude and phase of an order parameter that is related to the breaking of a continuous symmetry. We directly studied these modes in a supersolid quantum gas created by coupling a Bose-Einstein condensate to two optical cavities, whose field amplitudes form the real and imaginary parts of a U(1)-symmetric order parameter. Monitoring the cavity fields in real time allowed us to observe the dynamics of the associated Higgs and Goldstone modes and revealed their amplitude and phase nature.

Supersolid formation in a quantum gas breaking a continuous translational symmetry.

The concept of a supersolid state combines the crystallization of a many-body system with dissipationless flow of the atoms from which it is built. This quantum phase requires the breaking of two continuous symmetries: the phase invariance of a superfluid and the continuous translational invariance to form the crystal. Despite having been proposed for helium almost 50 years ago, experimental verification of supersolidity remains elusive.