Theory of selective excitation of multiple-quantum transitions

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Abstract
The question of whether a molecule can be made to absorb and emit photons only in groups of n is treated. Pulse sequences are introduced which in effect selectively induce the absorption of only groups of n photons. This causes only n‐quantum transitions even when many other transitions might be resonant. The technique involves repeated phase shifts of 2π/n in the radiation to build up the selected coherences and cancel all other coherences, and is applicable to a wide range of spectroscopic systems. Coherent averaging theory is extended to describe selective sequences and demonstrates that n‐quantum selectivity is possible to arbitrarily high order in the average Hamiltonian expansion. High‐order selectivity requires many phase shifts, however, and for this reason the residual nonselective effects of sequences which are selective to only a finite order are calculated. Selective sequences are applied to the multiple‐quantum NMR of oriented molecules, where in combination with time reversal sequences they produce a much more efficient transfer of the population differences into selected coherences than is obtainable by normal wideband pumping. For example, the 10‐quantum transition in a 10‐spin system can be enhanced by more than four orders of magnitude. Experiments on selective excitaiton of the 4‐quantum transitions in oriented benzene verify the expected enhancement.