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With the advances in high resolution and spin-resolved scanning tunneling microscopy as well as atomic-scale manipulation, it has become possible to create and characterize quantum states of matter bottom-up, atom-by-atom. This is largely based on controlling the particle- or wave-like nature of electrons, as well as the interactions between spins, electrons, and orbitals and their interplay with structure and dimensionality. We review the recent advances in creating artificial electronic and spin lattices that lead to various exotic quantum phases of matter, ranging from topological Dirac dispersion to complex magnetic order. We also project future perspectives in non-equilibrium dynamics, prototype technologies, engineered quantum phase transitions and topology, as well as the evolution of complexity from simplicity in this newly developing field.
Artificial lattices created by assembling atoms on a surface with scanning tunneling microscopy present a platform to create matter with tailored electronic, magnetic and topological properties. However, such artificial lattices studies to date have
Van der Waals materials can be easily combined in lateral and vertical heterostructures, providing an outstanding platform to engineer elusive quantum states of matter. However, a critical problem in material science is to establish tangible links be
The ability to apply GHz frequencies to control the quantum state of a single $P$ atom is an essential requirement for the fast gate pulsing needed for qubit control in donor based silicon quantum computation. Here we demonstrate this with nanosecond
Microscopic imaging of local magnetic fields provides a window into the organizing principles of complex and technologically relevant condensed matter materials. However, a wide variety of intriguing strongly correlated and topologically nontrivial m
Coupled atom-cavity arrays, such as those described by the Jaynes-Cummings Hubbard model, have the potential to emulate a wide range of condensed matter phenomena. In particular, the strongly correlated states of the fractional quantum Hall effect ca