Many-body quantum phases in programmable light potentials

We use ultracold atoms in a quantum-gas microscope setup with programmable light potentials to investigate many-body quantum phases. We first study commensurate and incommensurate 1D systems of only three to six interacting bosonic atoms prepared between two potential barriers. An in incommensurate system is then deterministically created by dynamically shifting the barriers, reducing the number of available lattice sites while preserving the atom number. The incommensurate system is similar to a doped insulating state that exhibits atom transport and finite compressibility. We further explore the disordered Bose-Hubbard model on a square lattice, where we identify the Bose-glass phase via the Edwards-Anderson parameter. Using Talbot interferometry, we directly observe a reduction of the coherence length in the Bose-glass regime. Finally, we present new experiments on bosonic two-leg ladders. At half filling, we identify the Rung-Mott insulating phase through site-resolved measurements of rung parity and compressibility, complemented by modulation spectroscopy to probe the excitation gap.