Action spectroscopies use a readout created by the action of light on the molecules or material rather than optical absorption. Ultrafast 2D photocurrent and 2D fluorescence spectroscopies are two such action spectroscopies. Despite their utility, multidimensional action spectroscopies suffer from a background created by incoherent population mixing. These backgrounds appear when the action of one molecule impacts that of another, creating a signal that mimics a fourth-order population response but is really just the convolution of two linear responses. The background created by incoherent mixing is often much larger than the desired foreground signals. In this paper, we describe the physical mechanisms that give rise to the incoherent signals, drawing Feynman paths for each. There are three variations of incoherent signals, differing by their pulse ordering. They all have the same phase dependence as the desired fourth-order population signals and so cannot be removed by standard phase cycling, but they do differ in their polarization responses and dephasing times. We propose, and implement, a spectrometer design that eliminates the background signals for isotropically oriented samples, leaving only the desired fourth-order 2D action spectra. Our spectrometer utilizes a TWINS interferometer and a pulse shaper interferometer, each driven with a different white-light source so that the pulse pairs within each interferometer are phase stable, but not between the two. The lack of phase stability between the two interferometers eliminates two of the three incoherent responses. The third incoherent response is eliminated with the polarization scheme ⟨0, π/2, π/4, π/4⟩. Our spectrometer also enables both 2D photocurrent and 2D white-light spectra to be collected simultaneously, thereby enabling a direct comparison between action and optical detection under identical conditions and at the exact same position on the sample. Using this spectrometer and photovoltaic devices made from thin films of semiconducting carbon nanotubes, we demonstrate 2D photocurrent spectra free of incoherent background.
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