Model Predictions for Time-Resolved Transport Measurements Made near the Superfluid Critical Points of Cold Atoms and $K_3C_{60}$ Films

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.

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