Observation of three-photon resonances in NMR under four-field irradiation

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Abstract
Experimentally achievable conditions where only weak off-resonant fields are used to excite coherence in a two-level system are explored. A brief review of previous theoretical results useful in treating multifrequency irradiation sequences is provided. Using an approximation method based on the Floquet formalism we derive an expression for the effective field strength as a function of the phases and amplitudes of the applied irradiation fields. Some of these results are rederived and/or explained in a simplified manner. Under conditions of four-frequency irradiation, three-photon excitation of a two-level system in NMR is experimentally demonstrated on the spin-1/2 system of the 31P nucleus in phosphoric acid. The behavior of the three-photon resonance is explored as a function of all important experimental parameters. The results of these tests conform closely to the theoretical predictions. Possible uses of multifrequency irradiation schemes in NMR are suggested.