The "toolbox" of an ideal quantum emulator includes the ability to
control lattice structure, particle statistics, and interactions, at
sufficiently low temperatures, in a physical system whose fundamental
physical description is well understood. To create synthetic quantum
matter in a laboratory, one must identify a physical platform with
quantum degrees of freedom that are easily manipulated and probed. In
addition to well-known platforms based on ultracold atoms and ion traps,
we introduce an approach to creating synthetic quantum matter based on
reconfigurable nanostructures formed at the interface between two
normally insulating oxides, LaAlO3 and SrTiO3. The potential landscape
at this interface can be controlled with high precision (~ 2 nm),
smaller than the average electron separation. Electron-electron
interactions can be tuned between attractive (at low density) to
repulsive (at high density) regimes. The attractive regime leads to
electron pairing and superconductivity, while the latter leads to
fermionic behavior with repulsive interactions. Many elements of the
.quantum transport. toolbox have already been demonstrated, including
superconducting single-electron transistors, Fabry-Perot interference
and ballistic (quantized) transport of electrons and Cooper pairs in
dissipationless electron waveguides. The challenges and promise of this
approach will be described within the context of a parallel quest to
understand the underlying mechanism of electron pairing in SrTiO3.
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