Dephasing decay

Fig. 10. Dipolar dephasing decays of the branched Si without directly-bonded protons (a) and the with directly-bonded protons (b) of MSP before curing, and 2 Si signal of MSP cured at 400°C (c), respectively.

Smalley and co-workers have probed intramolecular vibrational relaxation by viewing the yields and the time-dependence of the fluorescence from Sj in alkylated benzenes. They focus attention on those ring modes whose vibrational frequencies are unshifted by alkylation these are vibrations with nodes at the alkylated ring carbon atom. The absorption lines are sharp, but as the alkyl chain is lengthened, the emission spectrum develops a broad relaxed component, while the intensity of the sharp unrelaxed resonance fluorescence diminishes in intensity as the intensity of the relaxed spectrum increases. The time-dependence of the relaxed and unrelaxed emission is found to be a single exponential decay, so unfortunately, the rapid intramolecular dephasing decay has not yet been followed. 

I CRS interferogram with a frequency of A = coj + 2c0j - cOq, where cOp is the detected frequency, coj is the narrowband frequency and coj the Raman (vibrational) frequency. Since cOq and coj are known, Wj may be extracted from the experimentally measured RDOs. Furthemiore, the dephasing rate constant, yj, is detemiined from the observed decay rate constant, y, of the I CRS interferogram. Typically for the I CRS signal coq A 0. That is, the RDOs represent strongly down-converted (even to zero... 

As the spins precess in the equatorial plane, they also undergo random relaxation processes that disturb their movement and prevent them from coming together fiilly realigned. The longer the time i between the pulses the more spins lose coherence and consequently the weaker the echo. The decay rate of the two-pulse echo amplitude is described by the phase memory time, which is the time span during which a spin can remember its position in the dephased pattern after the first MW pulse. Tyy is related to the homogeneous linewidth of the individual spin packets and is usually only a few microseconds, even at low temperatures. 

The transverse magnetization and the applied radiofrequency field will therefore periodically come in phase with one another, and then go out of phase. This causes a continuous variation of the magnetic field, which induces an alternating current in the receiver. Furthermore, the intensity of the signals does not remain constant but diminishes due to T and T2 relaxation effects. The detector therefore records both the exponential decay of the signal with time and the interference effects as the magnetization vectors and the applied radiofrequency alternately dephase and re-... 

The reference scan is to measure the decay due to spin-lattice relaxation. Compared with the corresponding stimulated echo sequence, the reference scan includes a jt pulse between the first two jt/2 pulses to refocus the dephasing due to the internal field and the second jt/2 pulse stores the magnetization at the point of echo formation. Following the diffusion period tD, the signal is read out with a final detection pulse. The phase cycling table for this sequence, including 2-step variation for the first three pulses, is shown in Table 3.7.2. The output from this pair of experiments are two sets of transients. A peak amplitude is extracted from each, and these two sets of amplitudes are analyzed as described below. 

The previous sections focused on the case of isolated atoms or molecules, where coherence is fully maintained on relevant time scales, corresponding to molecular beam experiments. Here we proceed to extend the discussion to dense environments, where both population decay and pure dephasing [77] arise from interaction of a subsystem with a dissipative environment. Our interest is in the information content of the channel phase. It is relevant to note, however, that whereas the controllability of isolated molecules is both remarkable [24, 25, 27] and well understood [26], much less is known about the controllability of systems where dissipation is significant [78]. Although this question is not the thrust of the present chapter, this section bears implications to the problem of coherent control in the presence of dissipation, inasmuch as the channel phase serves as a sensitive measure of the extent of decoherence. 

Thus in the zero dephasing case, 8s reduces to the Breit-Wigner phase of the intermediate state resonance, elaborated on in the previous sections. In the dissipative environment, it is sensitive also to decay and decoherence mechanisms, as illustrated later. 

Figure 15 illustrates the interplay between the time scales of intermediate state decay, final state decay, and dephasing in determining the photon energy dependence of 8s. The final state in Fig. 15 is chosen to satisfy the resonance condition when the intermediate state is resonantly excited, e/ e,- = 2(er — e,). 

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... 

Fig. 5 Radio frequency pulse sequences for measurements of Sj and Si in DSQ-REDOR experiments. The MAS period rR is 100 ps. XY represents a train of 15N n pulses with XY-16 phase patterns [98]. TPPM represents two-pulse phase modulation [99]. In these experiments, M = Nt 4, N2+ N3 = 48, and N2 is incremented from 0 to 48 to produce effective dephasing times from 0 to 9.6 ms. Signals arising from intraresidue 15N-13C DSQ coherence (Si) are selected by standard phase cycling. Signal decay due to the pulse imperfection of 15N pulses is estimated by S2. Decay due to the intermolecular 15N-I3C dipole-dipole couplings is calculated as Si(N2)/S2(N2). The phase cycling scheme can be found in the original figure and caption. (Figure and caption adapted from [45])...

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