  The conversion of nuclear matter to quark matter in the core of a rotating
neutron star alters its moment of inertia. Hence the epoch over which
conversion takes place will be signaled in the spin-down "signal_prl.tex" 581
lines, 22203 characters characteristics of pulsars. We find that an observable
called the braking index should be easily measurable during the transition
epoch and can have a value far removed (by orders of magnitude) from the
canonical value of three expected for magnetic dipole radiation, and may have
either sign. The duration of the transition epoch is governed by the slow loss
of angular momentum to radiation and is further prolonged by the reduction in
the moment of inertia caused by the phase change which can even introduce an
era of spin-up. We estimate that about one in a hundred pulsars may be passing
through this phase. The phenomenon is analogous to ``bachbending'' observed in
the moment of inertia of rotating nuclei observed in the 1970's, which also
signaled a change in internal structure with changing spin.
