Dephasing and Relaxation in Molecular Systems

We shall see in Chapter 7 that well-resolved sharp lines spectra of molecules can be obtained by incorporating them in suitable crystals. From such spectra, information about the interactions (vibronic coupling and spin-orbit coupling) and geometries (distortion) in the excited electronic state may be obtained. The results of these studies apply generally to static properties of the molecules, though the spectra also yield some information about relaxation phenomena. 

New developments in studying the dynamic interactions in such systems have occurred since the mid-eighties. These were mainly due to the use of tunable dye lasers, yielding time-resolved spectra. These were specifically important in the understanding of the dephasing processes in molecular mixed crystals, in particular those occurring on an ultrafast (picosecond) timescale. 

It is well known that by the uncertainty principle, the time-dependent processes give rise to the finite linewidth of an optical transition [170]. This homogeneous linewidth, however, can seldom be observed since crystal strain induces a spread in resonance frequencies, which exceeds in most cases the homogeneous width. The spectral line is then inhomogeneously broadened. 

Here the bath induces a random fluctuation of the transition frequency, but no energy is lost or transferred. By studying Tj -type processes, information about the interaction between the molecule and its environment (e.g., the phonons and transfer of excitation energy) can be obtained and the homogeneous from the inhomogeneous contribution of the fluorescence line can be separated. 

Dephasing can be studied either in the time domain (photon echo PE [171,172], optical free induction decay (OFID) [173, 174] or in the frequency domain (hole burning) [175-177]. With these techniques, the homogeneous broadening can be circumvented and the pure homogeneous width can be measured. 

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While in the frequency domain all the spectroscopic information regarding vibrational frequencies and relaxation processes is obtained from the positions and widths of the Raman resonances, in the time domain this information is obtained from coherent oscillations and the decay of the time-dependent CARS signal, respectively. In principle, time- and frequency-domain experiments are related to each other by Fourier transform and carry the same information. However, in contrast to the driven motion of molecular vibrations in frequency-multiplexed CARS detection, time-resolved CARS allows recording the Raman free induction decay (RFID) with the decay time T2, i.e., the free evolution of the molecular system is observed. While the non-resonant contribution dephases instantaneously, the resonant contribution of RFID decays within hundreds of femtoseconds in the condensed phase. Time-resolved CARS with femtosecond excitation, therefore, allows the separation of nonresonant and vibrationally resonant signals [151]. 

E>vib and Our also show up in the theory of spontaneous Raman spectroscopy describing fluctuations of the molecular system. The functions enter the CARS interaction involving vibrational excitation with subsequent dissipation as a consequence of the dissipation-fluctuation theorem and further approximations (21). Equations (2)-(5) refer to a simplified picture a collective, delocalized character of the vibrational mode is not included in the theoretical treatment. It is also assumed that vibrational and reori-entational relaxation are statistically independent. On the other hand, any specific assumption as to the time evolution of vib (or or), e.g., if exponential or nonexponential, is made unnecessary by the present approach. Homogeneous or inhomogeneous dephasing are included as special cases. It is the primary goal of time-domain CARS to determine the autocorrelation functions directly from experimental data. 

In Section II, we describe briefly the primary collisional effects, vibrational and rotational relaxation and dephasing processes, and discuss their influence on the time evolution of an electronically excited molecular system. 

Time resolved coherent anti-Stokes Raman spectroscopy of condensed matter has been recently extended to the femtosecond domain allowing direct and detailed studies of the fast relaxation processes of molecular vibrations in liquids. The vibrational phase relaxation (dephasing) is a fundamental physical process of molecular dynamics and has attracted considerable attention. Both experimental and theoretical studies have been performed to understand microscopic processes of vibrational dephasing. Developments in ultrafast coherent spectroscopy enables one now to obtain direct time-domain information on molecular vibrational dynamics. Femtosecond time-resolved coherent anti-Stokes Raman scattering measuring systems have been constructed (see Sec. 3.6.2.2.3) with an overall time resolution of less than 100 fs (10 s). Pioneering work has been per-... 

The Raman scattering (which is called resonance fluorescence when the final molecular state is identical to the initial one g)) is not, however, the only process resulting in spontaneous photon emission. If one repeats the above treatment in a density matrix formalism and allows for intermediate state dephasing, one obtains, for resonant excitation, a fluorescence contribution. In practice, in this case the doorway state is really (not virtually) excited and becomes populated for a significant time interval, as pointed out by Lee and Heller. The system becomes then sensitive to any phase-disturbing perturbation. As a consequence, due to dephasing, the scattering is no more a purely coherent two-photon process, and the Raman emission competes with a relaxed component which is usually called fluorescence. The fluorescence is then simply the spontaneous emission from populated excited states, which have completely lost the memory of the... 

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