Zero-quantum coherence, elimination

An alternative approach for the elimination of zero-quantum coherence is based on its evolution during periods of spin-locking in inhomogeneous Bq or Bj fields (Titman et al., 1990 Davis et al., 1993). This approach is particularly attractive, because it does not rely on time-consuming phasecycling schemes and variation of z-filter delays. Consider an inhomogeneous rf field with amplitude I f (r) that depends on the position r in the... 

More convenient approaches for the elimination of undesired coherences are possible in the case of frequency-selective irradiation schemes. If the spins that are involved in zero-quantum coherences resonate in well-separated spectral regions, the spins can be manipulated separately by selective (or semiselective) pulses (Vincent et al., 1992,1993). For example, a selective 90°(7) pulse transforms the antiphase combination (lyS — I Sy), which corresponds to zero-quantum coherence in the tilted frame, into (I S -t- lySy), whereas (—I S - lySy) is obtained if a 90° (7) pulse is used instead. Hence, a two-step phase cycle eliminates the antiphase terms... 

These purging pulses can be used to generate pure z-magnetization without contamination from zero-quantum coherence by following them with a 90°(y) pulse, as is shown in the NOESY sequence (b). Zero-quantum coherences present during the mixing time of a NOESY experiment give rise to troublesome dispersive contributions in the spectra, which can be eliminated by the use of this sequence. 

The presence of zero-quantum coherence during the mixing time can substantially distort NOE intensities. This coherence can not be removed with phasecycling or gradient pulses while preserving z-magnetisation. A z-filter scheme was proposed earlier for the elimination of the coherence. It utilises an adiabatic inversion pulse with linear frequency sweep applied simultaneously with a gradient. Cano et alP demonstrated that a better suppression is achieved with a z-filter cascade that combines several filter elements. The attainable suppression ration is then equal to the multiplication of the ratios for each element. 

The loss of coherence for an individual quantum system is always due to an entanglement with some other system and this holds even for a thermal reservoir. This can be seen from the following consideration assume that the quantum system studied is coupled to the reservoir with a coupling strength a and the reservoir relaxation rate is given by k. Standard adiabatic elimination of the reservoir then yields an atomic decay rate 7 = a2/k which tends to zero for an arbitrarily fast reservoir. This is due to the fact that for such a reservoir the combined system would truly remain in a product state and no entanglement would ever be built up. This may also be taken as a variant of quantum Zeno effect, in which the decay into an infinitely fast reservoir corresponds to very rapidly repeated measurements that prevent the spontaneous decay. 

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