Unified explanation for linear and nonlinear optical responses in β-carotene:: A sub-20-fs degenerate four-wave mixing spectroscopic study

The four-wave mixing signal of beta-carotene measured under the resonant excitation is reported. A clear coherent oscillation with a period of a few tens of femtoseconds was observed. We have estimated the line broadening function required to simulate this oscillation behavior. The parameters, including the solvation effect, which are essential for calculating the optical signals have also been determined. The validity of our simulation has been evaluated by comparing the theoretically calculated linear and nonlinear optical signals with the experimental results. It was found that in addition to the C - C and C = C stretching modes the methyl in-plane rocking mode significantly contributes to the optical responses of beta-carotene. Calculations based on the Brownian oscillator model were performed under the impulsive excitation limit, and we find that the memory of the vibronic coherence generated in the S-2 state is lost via relaxation processes, which include the S-1 state. Comparison between the simulation and experiment revealed that the two-photon absorption process plays an important role in the very early optical process taking place in beta-carotene. The vibronic decoherent time of the system is estimated to be 1 ps, which is about five times longer than the population lifetime of the S-2 state determined in the previous studies. The possible relationship between the lifetime of the vibronic coherence and the efficient energy transfer in light-harvesting antenna complexes is discussed.