Toward imaging with 2D spectra: Early waiting time measurements encode long-time spectral evolution

2D spectroscopies are powerful tools that disentangle overlapping excitations in linear and pump-probe spectra and reveal the dynamics of charge and energy flow, chemical kinetics, and even many-body interactions in complex systems. However, measuring these spectra with high precision and accuracy is difficult. For example, converging the statistical noise in signals at long waiting times becomes increasingly expensive, and extended laser exposure can cause sample degradation. Overcoming these fundamental challenges could enable the investigation of systems that are too delicate for study under multidimensional spectroscopies and accelerate the progress of 2D spectroscopy-based microscopies that could offer energetically resolved excitation dynamics with spatial resolution over heterogeneous environments. We address this problem by developing a new dimensionality reduction technique, the spectral generalized master equation (GME), that enables researchers to employ short-waiting time 2D spectra to determine and denoise the full evolution of 2D spectra over arbitrary waiting times with high temporal resolution. We demonstrate the applicability of our approach on theoretically generated and experimentally measured 2D electronic and 2D infrared spectra. We further show that our spectral GME cuts the reduces of experiments by multiple orders of magnitude and accurately removes statistical noise while circumventing the increasing convergence costs with longer waiting times.