  The two-dimensional superconductor formed at the interface between the
complex oxides, lanthanum aluminate (LAO) and strontium titanate (STO) has
several intriguing properties that set it apart from conventional
superconductors. Most notably, an electric field can be used to tune its
critical temperature (T$_c$), revealing a dome-shaped phase diagram reminiscent
of high T$_c$ superconductors. So far, experiments with oxide interfaces have
measured quantities which probe only the magnitude of the superconducting order
parameter and are not sensitive to its phase. Here, we perform phase-sensitive
measurements by realizing the first superconducting quantum interference
devices (SQUIDs) at the LAO/STO interface. Furthermore, we develop a new
paradigm for the creation of superconducting circuit elements, where local
gates enable in-situ creation and control of Josephson junctions. These
gate-defined SQUIDs are unique in that the entire device is made from a single
superconductor with purely electrostatic interfaces between the superconducting
reservoir and the weak link. We complement our experiments with numerical
simulations and show that the low superfluid density of this interfacial
superconductor results in a large, gate-controllable kinetic inductance of the
SQUID. Our observation of robust quantum interference opens up a new pathway to
understand the nature of superconductivity at oxide interfaces.

Mesoscale and Nanoscale Physics