  High resolution measurements of superfluid density and broadband
quasiparticle conductivity have been used to probe the low energy excitation
spectrum of nodal quasiparticles in underdoped YBCO. Penetration depth is
measured to temperatures as low as 0.05 K. Microwave conductivity is measured
from 0.1 to 20 GHz and is a direct probe of zero-energy quasiparticles. The
data are compared with predictions for a number of theoretical scenarios that
compete with or otherwise modify pure d-wave superconductivity, in particular
commensurate and incommensurate spin and charge density waves; d + i s and d +
i d superconductivity; circulating current phases; and the BCS--BEC crossover.
We conclude that the data are consistent with a pure d-wave state in the
presence of a small amount of strong scattering disorder, and are able to rule
out most candidate competing states either completely, or to a level set by the
energy scale of the disorder, ~ 4 K. Commensurate spin and charge density
orders, however, are not expected to alter the nodal spectrum and therefore
cannot be excluded.
