Quantum fluctuations and thec-axis optical conductivity of high-Tcsuperconductors

A theory of the frequency dependence of the interplane conductivity of a strongly anisotropic superconductor is presented. The form of the conductivity is shown to be a sensitive probe of the strength of quantum and thermal fluctuations of the phase of the superconducting order parameter. The temperature dependence of the superfluid stiffness and of the form of the absorbtion at frequencies of the order of twice the superconducting gap is shown to depend on the interplay between superconducting pairing, phase coherence, and the mechanism by which electrons are scattered. Measurements of the c-axis conductivity of high-${T}_{c}$ superconductors are interpreted in terms of the theory.