Oscillations in two-dimensional spectroscopy

Transition from electronic coherence to a vibrational mode.
Transition from electronic coherence to a vibrational mode made visible by Short Time Fourier Transform (see text).

Over the last years, a debate is going on whether the observation of long lasting oscillatory signals in two-dimensional spectra are reflecting vibrational of electronic coherences and how the functioning of the molecule is affected. Christoph Kreisbeck and I have performed a detailed theoretical analysis of oscillations in the Fenna-Matthews-Olson (FMO) complex and in a model three-site system. As explained in a previous post, the prerequisites for long-lasting electronic coherences are two features of the continuous part of the vibronic mode density are: (i) a small slope towards zero frequency, and (ii) a coupling to the excitonic eigenenergy (ΔE) differences for relaxation. Both requirements are met by the mode density of the FMO complex and the computationally demanding calculation of two-dimensional spectra of the FMO complex indeed predicts long-lasting cross-peak oscillations with a period matching h/ΔE at room temperature (see our article Long-Lived Electronic Coherence in Dissipative Exciton-Dynamics of Light-Harvesting Complexes or arXiv version). The persistence of oscillations is stemming from a robust mechanism and does not require adding any additional vibrational modes at energies ΔE (the general background mode density is enough to support the relaxation toward a thermal state). But what happens if in addition to the background vibronic mode density additional vibronic modes are placed within the vicinity of the frequencies related electronic coherences? This fine-tuning model is sometimes discussed in the literature as an alternative mechanism for long-lasting oscillations of vibronic nature. Again, the answer requires to actually compute two-dimensional spectra and to carefully analyze the possible chain of laser-molecule interactions. Due to the special way two-dimensional spectra are measured, the observed signal is a superposition of at least three pathways, which have different sensitivity for distinguishing electronic and vibronic coherences. Being a theoretical physicists now pays off since we have calculated and analyzed the three pathways separately (see our recent publication Disentangling Electronic and Vibronic Coherences in Two-Dimensional Echo Spectra or arXiv version). One of the pathways leads to an enhancement of vibronic signals, while the combination of the remaining two diminishes electronic coherences otherwise clearly visible within each of them. Our conclusion is that estimates of decoherence times from two-dimensional spectroscopy might actually underestimate the persistence of electronic coherences, which are helping the transport through the FMO network. The fine tuning and addition of specific vibrational modes leaves it marks at certain spots of the two-dimensional spectra, but does not destroy the electronic coherence, which is still there as a Short Time Fourier Transform of the signal reveals.

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