Based on simultaneous analysis of the frequency-resolved transient grating, peak shift, and echo width signals, we present a model for the third-order optical response of carotenoids including population dynamics and system-bath interactions. Our frequency-resolved photon echo experiments show that the model needs to incorporate the excited-state absorption from both the S-2 and the S-1 states. We apply our model to analyze the experimental results on astaxanthin and lycopene, aiming to elucidate the relation between structure and system-bath interactions. Our analysis allows us to relate structural motifs to changes in the energy-gap correlation functions. We find that the terminal rings of astaxanthin lead to increased coupling between slow molecular motions and the electronic transition. We also find evidence for stronger coupling to higher frequency overdamped modes in astaxanthin, pointing to the importance of the functional groups in providing coupling to fluctuations influencing the dynamics in the passage through the conical intersection governing the S-2-S-1 relaxation.
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