Femtosecond Time-Resolved Study of the Energy and Temperature Dependence of Hot-Electron Lifetimes in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{O}_{8+\mathit{\delta }}$

Electron lifetimes in a high- $T_c$ cuprate ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ are measured directly in time domain by the interferometric two-photon time-resolved photoemission technique. The lifetimes decrease from 60 to 10 fs in an energy range of 1.4 to 3.0 eV above $E_F$ with approximately $({E-E}_F{)}^{-2\mathrm{}}$ energy scaling of a normal, Fermi liquid metal. However, anomalous behavior shows up in a pronounced temperature dependence where the lifetimes of the 1.6 eV electrons decrease by 30% from 40 to 340 K. This study helps to define the nature of inelastic carrier scattering processes in the normal state of high- $T_c$ cuprates.