BCS-BEC Crossover Approach to the Optical Conductivity in high $T_c$ Superconductors

We address the finite frequency $\omega$ conductivity in the cuprates. We presume that the pseudogap arises from stronger-than-BCS attraction, which leads to non-condensed pairs above and below $T_c$. Our theoretical formalism, which is consistent with gauge invariance and the transverse f-sum rule, yields a mid infrared peak associated with the energy needed to break pairs. It also leads to a situation in which very high $\omega$ spectral weight participates in the formation of the condensate. These observations, along with others reported here are consistent with experiment.