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One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.

Units are at the heart of science and technology. Most measurements require units to express their result. The International System of Units (SI) provides a widely used coherent framework of units. While the present SI is fit for purpose for all measurements, it has several shortcomings. Most notably, the kilogram is defined via an artifact that limits its realization to a specific place and certain times. To solve this problem and to take advantage of advances in quantum metrology made in the last 50 years, a revision of the SI is planned. This revision will modify the foundation of the SI from base units to fundamental constants of nature. While the revision presents a huge shift in philosophy, the size of the units will not change, and hence the revision will go mostly unnoticed.