Spin Coherence Experiments

Fig. 2.9.7 Hahn spin-echo rf pulse sequence combined with bipolar magnetic field gradient pulses for hydrodynamic-dispersion mapping experiments. The lower left box indicates field-gradient pulses for the attenuation of spin coherences by incoherent displacements while phase shifts due to coherent displacements on the time scale of the experiment are compensated. The box on the right-hand side represents the usual gradient pulses for ordinary two-dimensional imaging. The latter is equivalent to the sequence shown in Figure 2.9.2(a).

As an alternative to QDs, silicon can be doped with single atom impurities, in particular phosphorus, which acts as an electron donor. Donors can be implanted individually with a precision of about 10 nm. Either the 31P nuclear spin or the unpaired electron can be used as qubits [63, 64]. An advantage of silicon is its widespread use in current electronics, meaning that QC might profit from methods and technologies already developed for their classical cousins . Also, spins in silicon can attain extremely high coherence times experiments on 28 Si-enriched silicon show spin coherence times T2 exceeding 10 s [65]. The read-out and coherent manipulation of individual spin qubits in silicon have been recently achieved [66]. 

The individual lines of the doublet signals relax with different rates due to the phenomenon of cross-correlated dipole-CSA relaxation. The CCR-rate can be extracted from the ratio of the intensity of the peaks /dipoie-csA = l/2tln (fhighfieldAowfieid)> where t is the time the selected coherences experience relaxation, and I denotes the signal intensities of the spin states. 

Because of the favorable cross-peak multiplet fine-structure, the HSQC experiment offers superior spectral resolution over the HMQC (heteronuclear multiple quantum coherence) experiment [13, 14], On the other hand, the HMQC experiment works with fewer pulses and is thus less prone to pulse imperfections. The real advantage of the HSQC experiment is for measurements of samples at natural isotopic abundance and without the use of pulsed field gradients, since the HSQC experiment lends itself to purging with a spin-lock pulse. Spin-lock purging in the HMQC experiment... 

The interesting thing is that the maximum intensity of the FID at the top of the echo is still less that that at the start of the FID not all of the coherence is recovered by refocusing in the second half of the spin echo. The part that is lost is the intrinsic decay, the loss of coherence due to pure T2 relaxation, a fundamental relaxation process. The spin echo simply gets back the losses due to inhomogeneity of the magnetic field (T losses). This gives us a method to measure 7 We could repeat the spin-echo experiment a number of times with different echo delays (t values) and start the acquisition of the FID at the top of the echo ... 

In 1964, the spin echo experiment was extended to the optical regime by the development of the photon echo experiment (3,4). The photon echo began the application of coherent pulse techniques in the visible and ultraviolet portions of the electromagnetic spectrum. Since its development, the photon echo and related pulse sequences have been applied to a wide variety of problems including dynamics and intermolecular interactions in crystals, glasses, proteins, and liquids (5-8). Like the spin echo, the photon echo and other optical coherent pulse sequences provide information that is not available from absorption or fluorescence spectroscopies. 

On timescales of less than or equal to that of spin-spin relaxation (T2) processes occur. T2 characterises the loss of phase coherence of the individual spin isochromats within the spin ensemble comprising the total magnetisation vector M0. A spin isochromat represents a group of spins that experiences the same homogeneous magnetic field and which, therefore, behaves in the same... 

FIGURE 12.8 Pulse sequence for the heteronuclear single quantum coherence experiment. See text for discussion of the state of the spin system at the times indicated. 

A modification of the HMQC referred to as the HMBC (Heteronuclear Multiple Bond Coherence) experiment can be optimized for transfer through multiple bonds based on the value of the multiple bond couplings, which is typically about 8 Hz for a three-bond coupling. The HMBC spectrum of dutasteride shown in Fig. 9 illustrates the utility of this experiment for assigning quaternary carbons, connecting isolated spin systems (e.g., Hig and Hig) to other spin systems in the molecule, and confirming assignments made from the COSY and HMQC spectra. 

For the 3Q experiment, the echo pathway 0 +3(ti) -l(/cti)-CP is selected by phase-cycling a series of 24 scans. The phase ( >i of the first pulse is then shifted by 60° for the additional 24 scans, in order to achieve the spin temperature inversion, as it results in a 3x60°= 180° shift of the coherence prior to the CP transfer. The same principle is applied to the selection of the 0 -5(ti) -l(/cti)-CP pathway in the 5QHETCOR experiment. In this case, the phase ( i in a series of 40 scans is shifted by 36° to achieve the spin temperature inversion. It should be noted that the phases applied to the CP pulse on the I channel follow those of the I spin coherence at time kti. This procedure... 

In the following, we show how an MQMAS echo is formed. The quadmpolar Hamiltonian under MAS will be derived as a perturbation to the strong static magnetic field Bq. The evolution of the density matrix under this Hamiltonian will be then shown to form an echo under a suitable selection of symmetric coherences. The manipulation of spin coherences by RF pulses will be assumed to be ideal here. The effects of nonidealities were discussed by the group of Vega. From the expression for the elements of the quadmpolar Hamiltonian, line narrowing by DOR experiment and echo formation by two alternative experiments, DAS and STMAS, will also be demonstrated and briefly discussed. Finally, some additional line narrowing schemes will be mentioned. 

In the STMAS experiment,like in MQMAS, spin coherences are manipulated rather than the spinning angle. However, instead of creating symmetric MQCs, the singlequantum satellite transition coherences. In — 1/2 >< n -f l/2l, are now excited. After an evolution period tj, these are then refocused with the symmetric CT SQCs evolving during t2- The relevant accumulated phase thus becomes... 

The command molecule has the highest priority in the internal hierarchy of the spin system definition. Next comes the nucleus statement, each magnetically non-equivalent nucleus is defined, one nucleus per line followed by the coupling interaction between nuclei, one interaction per line. It is also possible to define a non-thermal equilibrium spin system state such as produced in multiple quantum coherence experiments. The required coherence may be selected using the spin state definition rather than by a pulse sequence, this not only simplifies the pulse sequence but also reduces calculation times. Fig. 4.3 illustrates the general layout of a spin system file. In the case of a single spin system, the molecule and endmol commands are redundant and may be omitted. 

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