In 2D electronic spectroscopy studies, long-lived quantum beats have recently been observed in photosynthetic systems, and it has been suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning t
he electronic-vibrational quantum mixtures, the impact of protein-induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with vibrational modes in the resonant condition [J. Chem. Phys. 142, 212403 (2015)]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter-pigment coupling. In this study, we explore the impact of the fluctuations on electronic-vibrational quantum mixtures in a strongly coupled dimer. with an off-resonant vibrational mode. Toward this end, we calculate electronic energy transfer (EET) dynamics and 2D electronic spectra of a dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna-Matthews-Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein-induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the EET dynamics are demonstrated to be dominated by the environment and coupling between the 0-0 vibronic transitions as long as the Huang-Rhys factor of the vibrational mode is small.
Recently, nuclear vibrational contribution signatures in 2D electronic spectroscopy have attracted considerable interest, in particular as regards interpretation of the oscillatory transients observed in light-harvesting complexes. These transients h
ave dephasing times that persist for much longer than theoretically predicted electronic coherence lifetime. As a plausible explanation for this long-lived spectral beating in 2D electronic spectra, quantum-mechanically mixed electronic and vibrational states (vibronic excitons) were proposed by Christensson et al. [J. Phys. Chem. B 116, 7449 (2012)] and have since been explored. In this work, we address a dimer which produces little beating of electronic origin in the absence of vibronic contributions, and examine the impact of protein-induced fluctuations upon electronic-vibrational quantum mixtures by calculating the electronic energy transfer dynamics and 2D electronic spectra in a numerically accurate manner. It is found that, at cryogenic temperatures, the electronic-vibrational quantum mixtures are rather robust, even under the influence of the fluctuations and despite the small Huang-Rhys factors of the Franck-Condon active vibrational modes. This results in long-lasting beating behavior of vibrational origin in the 2D electronic spectra. At physiological temper- atures, however, the fluctuations eradicate the mixing and, hence, the beating in the 2D spectra disappears. Further, it is demonstrated that such electronic-vibrational quantum mixtures do not necessarily play a significant role in electronic energy trans- fer dynamics, despite contributing to the enhancement of long-lived quantum beating in 2D electronic spectra, contrary to speculations in recent publications.
Light harvesting components of photosynthetic organisms are complex, coupled, many-body quantum systems, in which electronic coherence has recently been shown to survive for relatively long time scales despite the decohering effects of their environm
ents. Within this context, we analyze entanglement in multi-chromophoric light harvesting complexes, and establish methods for quantification of entanglement by presenting necessary and sufficient conditions for entanglement and by deriving a measure of global entanglement. These methods are then applied to the Fenna-Matthews-Olson (FMO) protein to extract the initial state and temperature dependencies of entanglement. We show that while FMO in natural conditions largely contains bipartite entanglement between dimerized chromophores, a small amount of long-range and multipartite entanglement exists even at physiological temperatures. This constitutes the first rigorous quantification of entanglement in a biological system. Finally, we discuss the practical utilization of entanglement in densely packed molecular aggregates such as light harvesting complexes.
