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Perturbative nonlinear optical spectroscopies are powerful methods tounderstand the dynamics of excitonic and other condensed phase systems. Feynmandiagrams have long provided the essential tool to understand and interpretexperimental spectra and to organize the calculation of spectra for modelsystems. When optical pulses are strictly time ordered, only a small number ofdiagrams contribute, but in many experiments pulse-overlap effects areimportant for interpreting results. When pulses overlap, the number ofcontributing diagrams can increase rapidly, especially with higher orderspectroscopies, and human error is especially likely when attempting to writedown all of the diagrams. We present an automated Diagram Generator (DG) thatgenerates all of the Feynman diagrams needed to calculate any$n^{\text{th}}$-order spectroscopic signal. We characterize all perturbativenonlinear spectroscopies by their associated phase-discrimination condition aswell as the time intervals where pulse amplitudes are nonzero. Although the DGcan be used to automate impulsive calculations, its greatest strength lies inautomating finite pulse calculations where pulse overlaps are important. Weconsider third-order transient absorption spectroscopy and fifth-orderexciton-exciton interaction 2D (EEI2D) spectroscopy, which are respectivelydescribed by 6 or 7 diagrams in the impulsive limit but 16 or 240 diagrams,respectively, when pulses overlap. The DG allows users to automatically includeall relevant diagrams at relatively low computational cost, since the extradiagrams are only generated for the inter-pulse delays where they are relevant.For EEI2D spectroscopy, we show the important effects of including the overlapdiagrams.

Automatic Feynman diagram generation for nonlinear optical spectroscopies