  Novel physical phenomena arising at the interface of complex oxide
heterostructures offer exciting opportunities for the development of future
electronic devices. Using the prototypical LaAlO$_3$/SrTiO$_3$ interface as a
model system, we employ a single-step lithographic process to realize gate
tunable Josephson junctions through a combination of lateral confinement and
local side gating. The action of the side gates is found to be comparable to
that of a local back gate, constituting a robust and efficient way to control
the properties of the interface at the nanoscale. We demonstrate that the side
gates enable reliable tuning of both the normal-state resistance and the
critical (Josephson) current of the constrictions. The conductance and
Josephson current show mesoscopic fluctuations as a function of the applied
side gate voltage, and the analysis of their amplitude enables the extraction
of the phase coherence and thermal lengths. Finally, we realize a
superconducting quantum interference device in which the critical currents of
each of the constriction-type Josephson junctions can be controlled
independently via the side gates.
