Distinguishing Single-Particle Lifetime and Population Lifetime in a Cuprate Superconductor

We employ femtosecond time- and angle-resolved photoelectron spectroscopy to study optimally doped Bi-2212 (T$_{c} = $ 96 K). In the low excitation limit, the energy-resolved population lifetime displays abrupt changes near 60-80 meV both below and above T$_{c}$. Moreover, the lifetime near this characteristic energy is independent of excitation density. These behaviors are consistent with theories based on electron-boson interactions, which connect the population lifetimes to the single-particle lifetimes measured by equilibrium photoemission. However, the absolute values of these two quantities are different by one to two orders of magnitude. We further demonstrate that this discrepancy is independent of experimental techniques and materials, and point out the fundamental conceptual differences between the two lifetimes.