More than 30 years ago, Richard Feynman outlined his vision of a quantum

simulator for carrying out complex calculations on physical problems.

Today, his dream is a reality in laboratories around the world. This has

become possible by using complex experimental setups of thousands of

optical elements, which allow atoms to be cooled to Nanokelvin

temperatures, where they almost come to rest. Recent experiments with

quantum gas microscopes allow for an unprecedented view and control of

artificial quantum matter in new parameter regimes and with new probes.

In our atomic fermionic quantum gas microscope, we can detect both

charge and spin degrees of freedom simultaneously, thereby gaining

maximum information on the intricate interplay between the two in the

Fermi Hubbard model. In my talk, I will show how we can reveal hidden

magnetic order, directly image individual magnetic polarons, probe the

fractionalisation of spin and charge in dynamical experiments and reveal

the crossover from a polaronic metal to a Fermi liquid when continuously

increasing the doping in the system. For the first time we thereby have

access to directly probe non-local ‘hidden’ correlation properties of

quantum matter and to explore its real space resolved dynamical features

also far from equilibrium. Finally, I will discuss experiments on the

first realization of the Haldane phase in Hubbard ladder systems. Both

edge states and bulk string correlators enable us to reveal the special

topological features of this paradigmatic phase of matter.