Title: Model Predictions for Time-Resolved Transport Measurements Made near the Superfluid Critical Points of Cold Atoms and $K_3C_{60}$ Films,
Abstract: Recent advances in ultrafast measurement in cold atoms, as well as pump-probe
spectroscopy of $K_3 C_{60}$ films, have opened the possibility of rapidly
quenching systems of interacting fermions to, and across, a finite temperature
superfluid transition. However, determining that a transient state has
approached a second-order critical point is difficult, as standard equilibrium
techniques are inapplicable. We show that the approach to the superfluid
critical point in a transient state may be detected via time-resolved transport
measurements, such as the optical conductivity. We leverage the fact that
quenching to the vicinity of the critical point produces a highly time
dependent density of superfluid fluctuations, which affect the conductivity in
two ways. First, by inelastic scattering between the fermions and the
fluctuations, and second by direct conduction through the fluctuations, with
the latter providing a lower resistance current carrying channel. The
competition between these two effects leads to nonmonotonic behavior in the
time- resolved optical conductivity, providing a signature of the critical
transient state.