Quantum simulation with bosonic atoms in optical lattices under the microscope

Quantum gas microscopy provides unique access to the properties of quantum many-body system in- and out-of-equilibrium. Site-resolved density snapshots provide access to the full counting statistics of particle-number fluctuations in optical ladders, which we utilize in order to study the thermalization dynamics of hard-core bosons in quasi-1D systems, contrasting models with ballistic and chaotic dynamics. Using predictions from macroscopic fluctuation theory, we further extract diffusion constants from fluctuation growth in a far-from-equilibrium quench experiment. In addition, we demonstrate that optical superlattices can significantly expand the available toolbox by facilitating measurements of kinetic operators, such as kinetic energy or current. These operators can be measured and manipulated with single-bond resolution, which we demonstrate by locally rotating the measurement basis on isolated bonds using a digital-micromirror device. Moreover, single-shot readout provides information about full counting statistics and complex correlation functions. This paves the way for the implementation of efficient quantum state tomography and hybrid quantum computing protocols for itinerant particles on a lattice. We demonstrate the power of this technique by revealing the presence of local currents and current-current correlations in Hubbard models with artificial magnetic fields.