Time-dependent dephasing

This effect induces a time-dependent dephasing, and hence shifts the frequency ui t) ... 

A more phenomenological approach 25) allows to overcome this limitation. The space around each particle is divided between two regions the boundary is echo-time dependent. In the first one, near the particle, the gradients are too large for the refocusing pulses to be effective, so that the moments situated in this region will be rapidly dephased. These protons contribute a fast signal decay that is unobservable with MRI techniques. 

The excitation of the unlabeled dibromide followed by a time-delayed probe pulse gives a time-dependent intensity profile for the 202 amu signal. It shows a rapid decay component near time zero (time constant Tq) followed by a slower decay (xi). The slower decay exhibits a periodic coherent modulation (Xc) and a gradual dephasing (Fig. 20.4). 

Figure 7. (a) Concept of time-dependent alignment as a method for structural determination. Top Initial alignment at t = 0, dephasing, and recurrence of alignment at later times. Bottom Classical motion of a rigid prolate symmetric top. (b) Structures of stilbene and tryptamine-water complex from rotational coherence spectroscopy transients are shown, [see ref. 13]. 

In order to investigate the quantum number dependence of vibrational dephasing, an analysis was done on two systems C-I stretching mode in neat-CH3I and C-H mode in neat-CHCl3 systems. The C-I and C-H frequencies are widely different (525 cm-1 and 3020 cm-1, respectively) and so also their anharmonic constants. Yet, they both lead to a subquadratic quantum number dependence. The time-dependent friction on the normal coordinate is found to have the universal nonexponential characteristics in both systems—a distinct inertial Gaussian part followed by a slower almost-exponential part. 

The same arguments should hold well for C and H solutes in the case of CHCI3, because their individual masses are considerably different (C = 12 g/ mol and H = 1.008 g/mol), which means that H is more free to move than C and therefore the solvent influence on H is likely to have a dominant role in the determination of the C-H bond friction. Furthermore, C is actually shielded by the presence of three Cl atoms, a factor that has not been considered here. However, this is not expected to be serious because the dephasing is more sensitive to the friction dynamics of the H atom. The time-dependent friction profiles for H and C show similar strong bimodal behavior as in the case of CH3 and I systems. 

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]. 

In pure dephasing, the loss of coherence is caused by time-dependent perturbations of the vibrational frequency. Pure dephasing has been assumed in the earlier portions of this chapter and, in general, dominates vibrations in liquids. Within the cumulant approximation, both the Raman echo and FID decays can be calculated from Cffl(t) [Equations (4) and (13)]. Relating these measurement to properties of the solvent and solute requires a molecular model for Co,(t). 

A variably delayed probe pulse can be used to monitor the time-dependent vibrational oscillations and decay through coherent scattering ( diffraction ), yielding data like that shown in the simulation in Fig. 3a. In this simulation, the excitation and probe regions are overlapped spatially, and the decay of signal is due to damping and dephasing of the phonon-polariton response. From data of this form, the polariton frequency co and... 

For both time-dependent and steady-state models, coherent dephasing is taken into account by phenomenological terms in the off diagonal time derivatives of the DM elements that appear in the Liouville dynamics. In the time dependent model, increasing the donor or bridge decoherences decreases the yield asymmetry and... 

Magic angle spinning NMR spectra with variable cross polarization contact times were obtained on the intact, non-extracted sediments. The time-dependent spectra reveal subtle differences in organic carbon with depth differences not observed in single contact experiments. Dlpolar-dephased spectra of these same sediments indicate the presence of substantial amounts of substituted aromatic/olefinic carbons which are rapidly altered with depth. 

T2 relaxation causes dephasing of transverse magnetization as a result of time-dependent internal magnetic fields which modulate the resonance frequencies of individual magnetization components in an incoherent fashion (cf. Section 3.5). The resulting signal decay is irreversible. It cannot be refocused by an echo (cf. Section 2.2.1 and Fig. 2.2.10). Consequently, T2 filters are based on the formation of echoes [Hahl] to identify the irreversible signal decay. 

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