Ultrafast nonlinear spectroscopy

A comprehensive theoretical treatment of nonlinear spectroscopy, with an emphasis on theory applicable to ultrafast nonlinear spectroscopy. 

Theoretical calculations for ultrafast neat water spectroscopy are difficult to perform and difficult to interpret (because of the near-resonant OH stretch coupling). One classical calculation of the 2DIR spectrum even preceded the experiments [163] Torii has calculated the anisotropy decay [97], finding reasonable agreement with the experimental time scale. Mixed quantum/ classical calculations of nonlinear spectroscopy for many coupled chromo-phores is a daunting task. We developed the TAA for linear spectroscopy, and Jansen has very recently extended it to nonlinear spectroscopy [164]. We hope that this will allow for mixed quantum/classical calculations of the 2DIR spectrum for neat water and that this will provide the context for a molecular-level interpretation of these complex but fascinating experiments. 

Ultrafast vibrational spectroscopy offers a variety of techniques for unraveling the microsopic dynamics of hydrogen bonds occurring in the femto- to picosecond time domain. In particular, different vibrational couplings can be separated in nonlinear experiments by measuring vibrational dynamics in real-time. Both coherent vibrational polarizations and processes of population and energy relaxation have been studied for a number of hydrogen bonded systems in liquids [1],... 

If ultrafast nonlinear vibrational spectroscopy [1-3] has recently developed into an important tool providing original informations on the dynamics of weak hydrogen bonds (H-bonds), the simpler linear infrared (IR) vs(X—H) absorption spectroscopy spectra remains, however, to be an important method for the understanding of this dynamics. Considerable experimental and theoretical works have been done in this last field [4—17]. 

In this chapter we have surveyed recent experimental progress on the investigation of ultrafast nuclear wavepacket dynamics at surfaces. Nuclear (or vibrational) wavepackets of adsorbates are excited with ultrashort laser pulses, and subsequently their evolutions are probed with surface nonlinear spectroscopy such as 2PPE and SHG. These studies provide rich information on the initial stages of photoinduced... 

The conceptual framework for the - semiclassical simulation of ultrafast spectroscopic observables is provided by the Wigner representation of quantum mechanics [2, 3]. Specifically, for the ultrafast pump-probe spectroscopy using classical trajectories, methods based on the semiclassical limit of the Liouville-von Neumann equation for the time evolution of the vibronic density matrix have been developed [4-8]. Our approach [4,6-8] is related to the Liouville space theory of nonlinear spectroscopy developed by Mukamel et al. [9]. It is characterized by the ability to approximately describe quantum phenomena such as optical transitions by averaging over the ensemble of classical trajectories. Moreover, quantum corrections for the nuclear dynamics can be introduced in a systematic manner, e.g. in the framework of the entangled trajectory method [10,11]. Alternatively, these effects can be also accounted for in the framework of the multiple spawning method [12]. In general, trajectory-based methods require drastically less computational effort than full quantum mechanical calculations and provide physical insight in ultrafast processes. Additionally, they can be combined directly with quantum chemistry methods for the electronic structure calculations. 

For near-field imaging based on nonlinear or ultrafast spectroscopy, light pulses from a femtosecond Ti sapphire laser (pulse width ca. 100 fs, repetition rate ca. 

Ohta, K., M. Yang, and G. R. Fleming. 2001. Ultrafast exciton dynamics of J-aggregates in room temperature solution studied by third-order nonlinear optical spectroscopy and numerical simulations based on exciton theory. J. Chem. Phys. 115 7609-7621. 

One problem yet to be solved theoretically involves ultrafast echo and pump-probe experiments on H20. Jansen has extended the time-averaging approximation to nonlinear ultrafast spectroscopy [164], meaning that one is now in the position of calculating 2DIR spectra for liquid water, which would allow for direct comparison with results from the exciting new experiments [73, 74]. 

In recent years there has been significant interest in the extension of nonlinear optical spectroscopy to higher orders involving multiple time and/or frequency variables. The development of these multidimensional techniques is motivated by the desire to probe the microscopic details of a system that are obscured by the ensemble averaging inherent in linear spectroscopy. Much of the recent work to extend time domain vibrational spectroscopy to higher dimensionality has involved the use of nonresonant Raman-based techniques. The use of Raman techniques has followed directly from the rapid advancements in ultrafast laser technology for the visible and near-IR portions of the spectrum. Time domain nonresonant Raman spectroscopy provides access to an extremely... 

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