Abstract

Quantum simulation in optical lattices can address complex phases of strongly correlated electrons. With our quantum gas microscope, we measure snapshots of the quantum many-body wavefunction of Li-6 atoms by fully resolving the position and spin of each particle. I will present the application of this method to two quantum phases: The Haldane spin-1 phase is the prototype of a symmetry-protected topological phase, whose spin order is hidden in conventional two-point correlation functions. On our images, we can evaluate the characteristic string-correlator of this state and directly see the associated edge states of the system. In an antiferromagnetic 2d background, charge dopants get dressed by a surrounding cloud of ferromagnetic correlations and magnetically bound pairs of these polarons could be a building block of the intricate physics found in the cuprates. We directly image the spatial structure of the spin environment around individual holes and recently observed bound pairs of holes when constraining the motion of holes to 1D while keeping spin order two-dimensional.