  It is believed that the core of a neutron star can be host to various novel
phases of matter, from nucleon superfluid phase to exotic high baryon density
quantum chromodynamics (QCD) phases. Different observational signals for such
phase transitions have been discussed in the literature. Here, we point out a
unique phenomenon associated with phase transition to a superfluid phase, which
may be the nucleon superfluid phase or a phase like the CFL phase, allowing for
superfluid vortices. In any superfluid phase transition, a random network of
vortices forms via the so-called Kibble-Zurek mechanism, which eventually
mostly decays away, finally leaving primarily vortices arising from the initial
angular momentum of the core. This transient, random vortex network can have a
non-zero net angular momentum for the superfluid component, which will
generally be oriented in an arbitrary direction. This is in contrast to the
final vortices, which arise from initial rotation and hence have the initial
angular momentum of the neutron star. The angular momentum of the random vortex
network is balanced by an equal and opposite angular momentum in the normal
fluid due to the conservation of angular momentum, thereby imparting an
arbitrarily oriented angular momentum component to the outer shell of the
neutron star. This will affect the pulse timing and pulse profile of a pulsar.
These changes in the pulses will decay away in a characteristic manner such
that the random vortex network decays, obeying specific scaling laws leading to
universal features for the detection of superfluid transitions occurring in a
pulsar core.
