Dephasing process

Fischer S. F., Laubereau A. Dephasing processes of molecular vibrations in liquids, Chem. Phys. Lett. 35, 6-12 (1975). 

As seen in Eqs. (59)—(61), dephasing processes introduce two new time scales into the dynamics, in addition to the intermediate state lifetime that determines the structure of 8s in the isolated molecule case. One is the time scale of pure dephasing, and the other is the lifetime of the final state. Equation (64) illustrates that the Tff dependence of 8s is a condensed phase effect that vanishes in the limit of no dephasing. The more careful analysis later shows that the qualitative behavior of the channel phase is dominated by the rpd/rrr and Tpd / [ ratios, that is, by the rate of dephasing as compared to the system time scales. 

By omitting the pure dephasing processes, which is warranted at low temperatures, the dephasing constant 1) ), in Eq. (III. 19) can be expressed, in terms of the population decay constants of the states v and v , as... 

Table 4.1. Various processes contributing to the spectral line broadening for local vibrations. Frequencies of collectivized local vibrations QK (solid arrows) are supposed to exceed phonon frequencies oiRq (dashed arrows) Ok > max oncq. For an extremely narrow band of local vibrations, diagrams A and B respectively refer to relaxation and dephasing processes, whereas diagrams C account for the case realizable only at the nonzero band width for local vibrations.

The strain-stress relationship ay = Cykfiki is valid when strain is instantaneously provoked by stress, i.e., no dephasing process occurs. In fact, it was observed that the magnitude of acoustic waves decreased as a function of the travelling distance. Introducing a damping term proportional to the time course of strain variations can solve this discrepancy ... 

The ultrafast laser pulse excites many vibrational modes of the metal carbonyl simultaneously (i.e., the vibrational modes are phase-coupled). Are the subsequent ligand motions coherent or do ultrafast dephasing processes hinder coherent motions ... 

Figure 3. Field-matter interactions for a pair of electronic states. The zero and first excited vibrational levels are shown for each state (A). The fields are resonant with the electronic transitions. A horizontal bar represents an eigenstate, and a solid (dashed) vertical arrow represents a single field-matter interaction on a ket (bra) state. (See Refs. 1 and 54 for more details.) A single field-matter interaction creates an electronic superposition (coherence) state (B) that decays by electronic dephasing. Two interactions with positive and negative frequencies create electronic populations (C) or vibrational coherences either in the excited (D) or in the ground ( ) electronic states. In the latter cases (D and E) the evolution of coherence is decoupled from electronic dephasing, and the coherences decay by the vibrational dephasing process.

A more general approach is required to interpret the current experiments, Jean and co-workers have developed multilevel Redfield theory into a versatile tool for describing ultrafast spectroscopic experiments [22-25], In this approach, terms neglected at the Bloch level play an important role for example, coherence transfer terms that transform a coherence between levels i and j into a coherence between levels j and k ( /t - = 2) or between levels k and l ( f - j - 2, k-j = 2) and couplings between populations and coherences. Coherence transfer processes can often compete effectively with vibrational relaxation and dephasing processes, as shown in Fig. 4 for a single harmonic well, initially prepared in a superposition of levels 6 and 7. The lower panel shows the population of levels 6 and 7 as a function of time, whereas the upper panels display off-diagonal density matrix ele-... 

Because the induced NMR signal after switching off the 90° RF pulse decays so rapidly as mentioned above, spin echoes are often detected in many practical pulse sequences for MRI visualization. Spin echo is formed by an additional RF pulse applied to the sam-ple.The additional RF pulse is applied after an evolution period, r. This RF pulse that gives rise to inversion of the magnetization components causes the spins to rephrase and is thus referred to the 180° RF pulse as shown in Fig. 2. This rephrasing process contributes to recover the transverse magnetization which had lost in dephasing process and results in the formation of an echo . We detected the echo by the receiver coil. The time from when the 90° RF pulse is applied to when the echo forms is referred to as the echo time , TE and is equal to twice the time between the 90° and 180° pulses, i.e. 2r. 

The prevalence of structural compared with dynamical information arises from a scarcity of appropriate spectroscopic techniques. For example, the measurement process in NMR spectroscopy takes place on a millisecond timescale. The dominating part of the fluctuation correlation function responsible for dephasing processes, on the other hand, decays on the picosecond timescale, so that spin transitions are strongly in the motional... 

Finally, all examples discussed below have in common the property that all the phenomena are ultrafast the time scale of observation is limited by the Ti time of the vibrational manifold. In the case of electronic transition echoes this is not such a limitation since the lifetimes of electronically excited states are generally long compared with the various dephasing processes that are considered. 

Thus the Raman echo adds vital new information on the dephasing process. This fact does not obviate Raman line shape or FID measurements. Because of their relative simplicity and experimental ease, these techniques remain valuable tools. However, using them in comparison with the Raman echo [Equations (11) and (12)] provides a much more complete and less model-dependent picture of vibrational dephasing than is possible with line shape or FID measurements alone. 

As soon as the coherent superposition is created, it begins to decay due to dephasing processes. The amount of coherence remaining after a period r is measured with a probe (II) Laser pulse. This pulse stimulates the coherent superposition to emit an anti-Stokes (AS) pulse as it returns to the ground state. The decay of the coherence is recorded by measuring the intensity of the AS pulse as the time period r is increased. 

The choice of laser system is dictated by the considerations outlined above. High-energy pulses of two different frequencies are needed, and good temporal synchronization between the pulses is essential. A pulse width of 0.3-1.0 ps is adequate to resolve most dephasing processes. Good mode quality is important to minimize self-focusing. 

Figure 11 Raman FID of the yym-methyl stretch in 50 50 CH3LCDCI3 showing a nonexponential decay (points). The fit (solid curve) is a combination of fast (T2 = 2.0 ps) and slow (A = 4.25 cm-1) dephasing processes. (From Ref. 4.)...

A quantitative fit of the VE theory to the toluene data is shown in Fig. 20. In addition to the VE dephasing, an additional temperature-independent, fast-modulation dephasing process had to be included. Several reasonable mechanisms exist for this additional dephasing the population lifetime and inertial dynamics acting through phonon scattering or through imperfect correlations in the solvent. The theory reproduces... 

Figure 20 The VE theory of dephasing fit to Raman-FID data on toluene (see Fig. 15). The entire range of data is fit with only three temperature-independent parameters the solvent s high-frequency elastic modulus, a solvent-solute coupling constant, and a homogeneous dephasing time. A temperature-independent homogeneous dephasing process is assumed in addition to the VE mechanism.

The outline of this review is as follows. In Section II we discuss the Pauli master equation and we show how to derive it from a coherent quantum mechanical process through the addition of a dephasing process. 

Since the pulse time is so short (see Sec. 3.6.2.2.3) one can coherently excite many vibrational modes at a time and monitor relaxation processes in real time. The first reported femtosecond time-resolved CARS experiments (Leonhardt et al., 1987 Zinth et al., 1988) showed beautiful beating patterns and fast decays of the coherent signal for several molecular liquids. The existence of an intermolecular coherence transfer effect was suggested from the analysis of the beating patterns (Rosker et al., 1986). Subsequent studies by Okamoto and Yoshihara (1990) include the vibrational dephasing of the 992 cm benzene mode. A fast dephasing process was found that is possibly related to... 

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