  Many superconducting technologies such as rapid single flux quantum computing
(RSFQ) and superconducting quantum interference devices (SQUIDs) rely on the
modulation of nonlinear dynamics in Josephson junctions for functionality. More
recently, however, superconducting devices have been developed based on the
switching and thermal heating of nanowires for use in fields such as single
photon detection and digital logic. In this paper, we use resistive shunting to
control the nonlinear heating of a superconducting nanowire and compare the
resulting dynamics to those observed in Josephson junctions. We show that
interaction of the hotspot growth with the external shunt produces high
frequency relaxation oscillations with similar behavior as observed in
Josephson junctions due to their rapid time constants and ability to be
modulated by a weak periodic signal. In particular, we use a microwave drive to
pull and mix the oscillation frequency, resulting in phase locked features that
resemble the AC Josephson effect. New nanowire devices based on these
conclusions have promising applications in fields such as parametric
amplification and frequency multiplexing.
