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In complex materials various interactions play important roles in determiningthe material properties. Angle Resolved Photoelectron Spectroscopy (ARPES) hasbeen used to study these processes by resolving the complex single particleself energy $\Sigma(E)$ and quantifying how quantum interactions modify bareelectronic states. However, ambiguities in the measurement of the real part ofthe self energy and an intrinsic inability to disentangle various contributionsto the imaginary part of the self energy often leave the implications of suchmeasurements open to debate. Here we employ a combined theoretical andexperimental treatment of femtosecond time-resolved ARPES (tr-ARPES) and showhow measuring the population dynamics using tr-ARPES can be used to separateelectron-boson interactions from electron-electron interactions. We demonstratethe analysis of a well-defined electron-boson interaction in the unoccupiedspectrum of the cuprate Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ characterized by anexcited population decay time constant $\tau_{QP}$ that maps directly to adiscrete component of the equilibrium self energy not readily isolated bystatic ARPES experiments.

Energy dissipation in the time domain governed by bosons in a correlated material