Nodal Quasiparticle Lifetime in the Superconducting State ofBi2Sr2CaCu2O8+δ

We have measured the complex conductivity $\sigma$ of a ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ thin film between 0.2 and 0.8 THz. We find $\sigma$ in the superconducting state to be well described as the sum of contributions from quasiparticles, condensate, and order parameter fluctuations which draw $30\%$ of the spectral weight from the condensate. An analysis based on this decomposition yields a quasiparticle scattering rate on the order of $k_{B}T/ħ$ for temperatures below $T_c$.