  Coherent quantum phase slips are expected to lead to a blockade of dc
conduction in sufficiently narrow superconducting nanowires below a certain
critical voltage. We present measurements of NbN nanowires in which not only is
a critical voltage observed, but also in which this critical voltage may be
tuned using a side-gate electrode. The critical voltage varies periodically as
the applied gate voltage is varied. While the observations are qualitatively as
expected for quantum interference between coherent quantum phase slip elements,
the period of the tuning is orders of magnitude larger than expected on the
basis of simple capacitance considerations. Furthermore, two significant abrupt
changes in the period of the variations during measurements of one nanowire are
observed, an observation which constrains detailed explanations for the
behaviour. The plausibility of an explanation assuming that the behaviour
arises from granular Josephson junctions in the nanowire is also considered.
