Interfaces between complex oxides are emerging as one of the most interesting playgrounds in condensed matter physics. In this special setting, in which translational symmetry is artificially broken, a variety of novel electronic phases can be promoted. Theoretical studies predict complex phase diagrams and suggest the key role of the carrier density in determining the systems ground states. A particularly fascinating system is the interface between the insulators LaAlO$_{3}$ and SrTiO$_{3}$, which displays conductivity with high mobility. Recently two possible ground states have been experimentally identified: a magnetic state and a two dimensional (2D) superconducting condensate. In this Letter we use the electric field effect to explore the phase diagram of the system. The electrostatic tuning of the carrier density allows an on/off switching of superconductivity and drives a quantum phase transition (QPT) between a 2D superconducting state and an insulating state (2D-QSI). Analyses of the magnetotransport properties in the insulating state are consistent with weak localisation and do not provide evidence for magnetism. The electric field control of superconductivity demonstrated here opens the way to the development of novel mesoscopic superconducting circuits
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