This letter reports a straightforward means of collecting two-dimensional electronic (2D-E) spectra using optical tools common to many research groups involved in ultrafast spectroscopy and quantum control. In our method a femtosecond pulse shaper is used to generate a pair of phase stable collinear laser pulses which are then incident on a gas or liquid sample. The pulse pair is followed by an ultrashort probe pulse that is spectrally resolved. The delay between the collinear pulses is incremented using phase and amplitude shaping and a 2D-E spectrum is generated following Fourier transformation. The partially collinear beam geometry results in perfectly phased absorptive spectra without phase twist. Our approach is much simpler to implement than standard non-collinear beam geometries, which are challenging to phase stabilize and require complicated calibrations. Using pulse shaping, many new experiments are now also possible in both 2D-E spectroscopy and coherent control.

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Adaptive femtosecond control experiments are expanding the possibilities for using laser pulses as photophysical and photochemical reagents. However, because of the large number of variables necessary to perform these experiments (usually 100-200), it has proven difficult to elucidate the underlying control mechanisms from the optimized pulse shapes. If adaptive control is to become a widespread tool for examining chemical dynamics, methods must be developed that reveal latent control mechanisms. This manuscript presents a generally applicable method for dimension reduction of adaptive control experiments based on partial least squares regression analysis (PLS) of the normalized covariance matrix of the total data set. When applied to experimental results obtained in our laboratory, it shows that only seven fundamental dimensions from an original 208-dimension search space are needed to account for approximately 90% of the variance in the observed fitness of 11,700 laser-pulse shapes explored during the optimization experiment. Furthermore, the seven dimensions have a remarkable regularity in their functional form. It is anticipated that this work will facilitate theoretical treatments directly linking the optimal fields to control mechanisms, allow quantitative comparisons of independent control results, and suggest new experimental methods for rapid adaptive searches.

To design methodologies that will allow researchers to directly correlate the results of adaptive control experiments with physiochemical control pathways in arbitrary complex molecular systems it is imperative that prototype systems are developed and that exigent control pathways are understood. We have been interested in the results of adaptive control experiments in our laboratory involving the maximization of a ratio of two experimental observables: (1) the thermalized emission from the solution-phase coordination complex [Ru(dpb)3](PF6)2 and (2) the second harmonic signal (a purely intensity-dependent phenomenon) of the shaped laser fields. Using a rational pulse shaping strategy, we have made a measurement of the ratio spectrum (in essence the two-photon absorption cross section) for the molecule [Ru(dpb)3](PF6)2 in a room temperature solution of acetonitrile. This spectrum is highly varied across the accessible two-photon power spectrum of our broad-band laser pulses and demonstrates the existence of a control pathway wherein a shaped laser field can manipulate excited-state population (with respect to SHG) by conforming to the second-order spectral response of the molecule in solution. We show that our adaptive control algorithm is capable of taking advantage of these control pathways using simulated adaptive control experiments. Finally, we measure second-harmonic spectra of shaped laser fields discovered during an adaptive control experiment and show that these agree with simulation. These results suggest that our adaptive control experiment can be understood in the context of the elucidated spectral control pathway.

Adaptive laser pulse shaping has proven to be expeditious for discovering laser pulse shapes capable of manipulating complex systems. However, if adaptive control is to be a valuable interrogative technique that informs physical and chemical research, methods that make it possible to infer mechanistic information from experimental results must be developed. Here, we demonstrate multivariate statistical analysis to extract a single control variable from results of a 137-parameter adaptive laser pulse-shaping optimization of multiphoton electronic excitation in a ruthenium(II) coordination complex in solution. We show that this single variable can be used to linearly manipulate the observed fitness, which is determined by the ratio of molecular emission to second harmonic generation of the laser pulse, over the range explored during the adaptive optimization. Further, manipulation of this variable reveals the latent control mechanism. For this system, that mechanism entails focusing the second harmonic power spectrum of the laser field in a spectral region where the probability of two-photon absorption by the molecule is also large. The statistical tools developed are general and will help elucidate control mechanisms in future adaptive pulse-shaping experiments.