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.