  Quantum ground states which arise at atomically controlled oxide interfaces
provide an opportunity to address key questions in condensed matter physics,
including the nature of two-dimensional (2D) metallic behaviour often observed
adjacent to superconductivity. At the superconducting LaAlO3/SrTiO3 interface,
a metallic ground state emerges upon the collapse of superconductivity with
field-effect gating. Strikingly, such metallicity is accompanied with a
pseudogap. Here, we utilize independent control of carrier density and disorder
of the interfacial superconductor using dual electrostatic gates, which enables
the comprehensive examination of the electronic phase diagram approaching zero
temperature. We find that the pseudogap corresponds to precursor pairing, and
the onset of long-range phase coherence forms a 2D superconducting dome as a
function of the dual gate voltages. The gate-tuned superconductor-metal
transitions are driven by macroscopic phase fluctuations of Josephson coupled
superconducting puddles.
