The realization of fully controlled, coherent many-body quantum systems is an outstanding challenge in science and engineering. Quantum optical systems, such as photons, atoms or atoms-like systems, hold great promises to achieve this goal. With novel tools and functionalities that have been developed in recent years, they allow the realization of quantum simulators, providing insights into strongly correlated quantum systems, as well as the implementation of ideas from quantum information science.
In this talk I want to discuss a few examples that highlight how state-of-the-art quantum optical technology can be employed to address questions of fundamental interest in condensed matter physics and quantum information, in particular, how to create, measure and make use of entanglement in many body systems. Entanglement is at the heart of most quantum information protocols, it underlies the complexity of simulating quantum physics on classical computers, and it is used as a theoretical tool to characterize exotic states of matter. I will first discuss protocols employing tools available in cold atom experiments that allow to directly measure entanglement in these systems. These are based on the possibility to interfere several copies of the same quantum many-body state and give access to entanglement in terms of Renyi entropies or even the entanglement spectrum Then I will present different ways to create highly entangled states of atoms or photons and using them for quantum simulation and computing. To this end I will first discuss the physics of arrays of individually trapped Rydberg atoms ,that allow to explore a variety of condensed matter models, and show how these systems can be used to naturally realize quantum annealers for classical optimization problems. Finally I want to present a novel way to create highly entangled states of photons by sequentially generating and correlating photons using a single quantum emitter in a waveguide QED setting. I will show that using delayed quantum feedback dramatically expands the class of achievable photonic quantum states in such settings and in particular allows to generate states that are universal resources for quantum computation.