Mapping multidimensional electronic structure and ultrafast dynamics with single-element detection and compressive sensing.

Compressive sensing allows signals to be efficiently captured by exploiting their inherent sparsity. Here we implement sparse sampling to capture the electronic structure and ultrafast dynamics of molecular systems using phase-resolved 2D coherent spectroscopy. Until now, 2D spectroscopy has been hampered by its reliance on array detectors that operate in limited spectral regions. Combining spatial encoding of the nonlinear optical response and rapid signal modulation allows retrieval of state-resolved correlation maps in a photosynthetic protein and carbocyanine dye. We report complete Hadamard reconstruction of the signals and compression factors as high as 10, in good agreement with array-detected spectra. Single-point array reconstruction by spatial encoding (SPARSE) Spectroscopy reduces acquisition times by about an order of magnitude, with further speed improvements enabled by fast scanning of a digital micromirror device. We envision unprecedented applications for coherent spectroscopy using frequency combs and super-continua in diverse spectral regions.