“…It is worthwhile to consider the two-pulse variant of population-detected spectroscopy, that is phase-locked double-pump population-detected spectroscopy, in some detail. This technique, pioneered in femtosecond ensemble molecular spectroscopy by Scherer and co-workers, was extended to single-molecule spectroscopy by van Hulst and co-workers , and to single-molecule microscopy by Fujiwara and Zhou et al , Double-pump population-detected signals were simulated for a number of systems, from molecules − ,− to antenna complexes. − These signals can be calculated via eq through the numerical solution of driven TDSEs or MEs with a system–field interaction Hamiltonian containing two pump pulses separated by the time delay τ. It is not necessary to perform a phase decomposition of the double-pump population-detected signal, because it can be conveniently decomposed into population and coherence contributions. , If, for example, the pump pulses are temporally well separated and contributions from the states of manifold {II} can be neglected, the DW approximation yields the double-pump population-detected signal in the form S ( τ ) = A ( τ ) + ( B false( τ false) e i φ + B * false( τ false) e − i φ ) e − γ τ Here A (τ) is the contribution which results from the evolution of the chromophore in electronic population, B (τ) is the coherence contribution, φ is the relative phase of the pump pulses, and γ is the electronic dephasing rate.…”