Solid-state magnetic traps and lattices

We propose and analyze magnetic traps and lattices for electrons in semiconductors. We provide a general theoretical framework and show that thermally stable traps can be generated by magnetically driving the particle's internal spin transition, akin to optical dipole traps for ultra-cold atoms. Next we discuss in detail periodic arrays of magnetic traps, i.e. magnetic lattices, as a platform for quantum simulation of exotic Hubbard models, with lattice parameters that can be tuned in real time. Our scheme can be readily implemented in state-of-the-art experiments, as we particularize for two specific setups, one based on a superconducting circuit and another one based on surface acoustic waves.