: ( R^(3) ) is the molecule’s memory function for three successive kicks from the electric field. Each ( t_i ) is a waiting time where the molecule evolves under its own Hamiltonian (no laser).
You can watch a molecule change shape or break a bond while it's happening. The "Dummy" Summary : ( R^(3) ) is the molecule’s memory
to explain how we can "reverse" time to eliminate spectral broadening. UCI Department of Chemistry Core Concepts of Nonlinear Spectroscopy A Practical Approach or: Mukamel for Dummies The "Dummy" Summary to explain how we can
Confusing ( T_1 ) (population lifetime) and ( T_2 ) (dephasing time). Fix: ( T_2 ) = ( 1/( \textlinewidth ) ). ( T_1 ) = how long excited state lives. Always ( T_2 \le 2T_1 ). If your ( T_2 ) is shorter than ( 2T_1 ), you have pure dephasing. ( T_1 ) = how long excited state lives
Mukamel visualizes these nested commutators as (ket and bra evolve separately). For third-order, there are exactly 5 distinct diagrams that survive in the rotating wave approximation:
Don't get bogged down in the Greek letters. Mukamel is essentially describing a conversation between light and matter. The pulses are the questions, and the signal is the molecule’s answer.