Differentiation of True Nonlinear and Incoherent Mixing of Linear Signals in Action-Detected 2D Spectroscopy

Abstract

Phase modulation and phase cycling schemes have been commonly used in electronic two-dimensional (2D) spectroscopy where the observables are incoherent signals such as fluorescence or photocurrent. Although the methods have distinct advantages compared to the coherent signal-detected 2D spectroscopy in sensitivity, possibility to measure spectra from isolated quantum systems and direct visualization of the contributions from the different states to the action signals, and ambiguities in interpreting the spectra have emerged. Recent reports have shown that apart from the nonlinear signals from the four pulse interactions, mixing of the linear signals due to nonlinear population dynamics during the long measurement time of the action signals can also contribute to the measured 2D spectra. Exciton–exciton annihilation has been considered to play a major role in the mixing of the linear signals. Thus, it has become important to further characterize the origin of the measured signals. Here, using a nonperturbative simulation of the 2D spectra based on the time evolution of the density matrix in the Lindblad form, we show that the exciton–exciton annihilation contributes to the measured signal only if the quantum yields of the different excited states are not the same. In these cases, the mixed signals can be distinguished from the true nonlinear signals if the phases are measured with respect to the linear signals. In action-detected 2D spectra, the mixed signals have a π phase shift relative to the true nonlinear signals. A detailed discussion on the experimental implementations of the schemes used in the simulations is also provided.

Vibronic coherence contributes to photocurrent generation in organic semiconductor heterojunction diodes

“…In distinction to our method for nonlinear imaging of photocurrent for identifying recombination mechanisms 34,35 , where the amplitude of the nonlinear incoherent response is used, here the phase of the photocurrent is extracted by varying the interpulse time delays. This has been shown to account for the coherent nonlinear interactions in this type of spectroscopic measurement 36,37 . For all the investigated devices here, the same setup with a temporal resolution of about 15 fs and identical experimental conditions have been used.…”

Phase-Modulated Rapid-Scanning Fluorescence-Detected Two-Dimensional Electronic Spectroscopy

“…In phase-modulated 2D measurements based on conventional lock-in detection, the phase is typically adjusted such that the real parts of the signal are maximized during the overlap of the pulses ( " = $ = 0). 9,15 As discussed by Karki and coworkers, absolute signal phase determination may enable the separation of true nonlinear signals from those produced by incoherent mixing of linear signals that can occur in actionbased 2D spectroscopy 25 . The simultaneous acquisition of two-quantum 2D spectra could be added to our approach, but would require digitization at considerably higher sampling rates to accommodate the higher frequency modulation of the two-quantum signals.…”

Two-dimensional spectroscopy beyond the perturbative limit: the influence of finite pulses and detection modes

“…From a purely theoretical point of view, the excited state populations have the same dependence on the interactions with the four pulses as the integrated fluorescence, meaning that the populations can be used as proxies for the measured signal. 35 In principle, one can distinguish between different excited state populations, but since it is difficult to detect fluorescence from distinct excited states, we neglect this possibility. 37 It is, however, relevant for other action spectroscopies.…”

“…34 However, careful analysis can differentiate between true nonlinear signals and incoherently mixed linear signals. 35 Experimentally, FD2D is currently more demanding than its counterpart. This is partly because two pulse delays need to be scanned instead of one.…”

“…Only a handful of papers have tackled the theory side of FD2D. 33,[35][36][37][38] Using the double-sided Feynman diagrams derived from perturbation theory, it is readily shown that each diagram from the traditional method has an equivalent diagram in fluorescence detection, which in addition has an extra set of excited state absorption (ESA) diagrams. 36 Although this knowledge forms an important basis for the interpretation of FD2D spectra, the differences do not end there.…”