  Controlling both the amplitude and phase of the quantum order parameter
({\psi}) in nanostructures is important for next-generation information and
communication technologies. The long-range coherence of attractive electrons in
superconductors render these materials as a nearly ideal platform for such
applications. To-date, control over {\psi} has remained limited to the
macroscopic scale, either by adjusting untunable materials properties, such as
film thickness, stoichiometry and homogeneity or by tuning external magnetic
fields. Yet, although local tuning of {\psi} is desired, the lack of electric
resistance in superconductors, which may be advantageous for some technologies
hinders convenient voltage-bias tuning. Likewise, challenges related to
nanoscale fabrication of superconductors encumber local tunability of {\psi}.
Here, we demonstrate local tunability of {\psi}, obtained by patterning with a
single lithography step a Nb nano superconducting quantum interference device
(nano-SQUID) that is biased at its nano bridges. Our design helped us reveal
also unusual electric characteristics-effective zero inductance, which is
promising for quantum technologies and nanoscale magnetic sensing. Finally, we
accompanied our experimental results by a semi-classical model, which not only
is extending the applicability of our devices, but is also useful for
describing planar nano-SQUIDs in general.
