  We explore the superconducting phase diagram of the two-dimensional electron
system at the LaAlO3/SrTiO3 interface by monitoring the frequencies of the
cavity modes of a coplanar waveguide resonator fabricated in the interface
itself. We determine the phase diagram of the superconducting transition as a
function of temperature and electrostatic gating, finding that both the
superfluid density and the transition temperature follow a dome shape, but that
the two are not monotonically related. The ground state of this 2DES is
interpreted as a Josephson junction array, where a transition from long- to
short-range order occurs as a function of the electronic doping. The synergy
between correlated oxides and superconducting circuits is revealed to be a
promising route to investigate these exotic compounds, complementary to
standard magneto-transport measurements.
