The second line shows that the S^3 CT sequence selectively inverts the
component ofSzmagnetization that is coupled to anIspin in the state.
A pictorial representation of the effect of the S^3 CT sequence on
coherences is illustrated using zero-quantum and double-quantum
coherences as an example in Fig. 2.7. The selective inversion is seen to
transferI–Sþcoherence intoI–S^ coherence andIScoherence into
IS^ coherence. An explicit calculation yields
ISþ )
I^ Sy
IS^ ,
IS )
I^ Sy
IS^ ,
½ 2 : 296
which is necessary to obtain the correct signs of the operators.
For completeness, the corresponding selective inversion across the
I – S a
I–S+
a
aa
ab
ba
bb
I–S–
b
aa
ab
ba
bb
pIaSy
pIaSy
I–Sb
FIGURE 2.7 Energy level diagram for S^3 CT pulse sequence. The S^3 CT
pulse sequence element is equivalent to a selective inversion across the
ji $
transition, as indicated by the curved arrows. (a) The S^3 CT
sequence converts zero-quantum coherence to single-quantum coherenceIS^.
(b) The S^3 CT sequence converts double-quantum coherence to single-quantum
coherenceI–S^.
2.7 PRODUCTOPERATORFORMALISM 101