Expanding Our View of Coherence Quantum Mechanics and Spherical Operators

4 EXPANDING OUR VIEW OF COHERENCE QUANTUM MECHANICS AND SPHERICAL OPERATORS 

Suppose that we are talking about a double-quantum transition in which both the proton and carbon change from the a state to the p state. This transition is thus from the aH c state to the PuPc state ol l lc two-spin, four-state system. This transition corresponds to DQC. Likewise, if the proton flips from ft to a while the carbon simultaneously flips from a to P, we have a zero-quantum transition (P ac to a Pc) because the total number of spins in the excited (ft) state has not changed. This transition corresponds to ZQC. What can we say about these mysterious coherences In Section 7.10, we encountered ZQC and DQC as intermediate states in coherence transfer, created with pulses from antiphase SQC  

Note that in the product operator — 21 Sy we have both spins, I and S ( ll and 13C) in the x-y plane, with the operators multiplied together. This means that both spins are undergoing transitions at the same time, so we have ZQC and DQC. We can convert ZQC and DQC back into observable SQC with a second pulse 

For example, on a 600-MHz spectrometer XH SQC precesses at 600 MHz, 13C SQC pre-cesses at 150 MHz, and H- C DQC precesses at 750 MHz. This makes sense because we are talking about a transition in which both XH and 13 C change from the a to the p state. Zero quantum coherence behaves in a similar way, but the precession rate is the difference between the two SQ precession frequencies  

The pairwise products of the operators Ix, ly, Sx, and can be expressed in terms of pure ZQC and DQC as follows  

---