CONTINUOUS WAVE MULTIQUANTUM ELECTRON-PARAMAGNETIC RESONANCE SPECTROSCOPY .3. THEORY OF INTERMODULATION SIDE-BAND

The interaction of a spin 1/2 system with two continuous wave transverse electromagnetic fields is studied using the dressed-atom formalism and the Floquet theory. The equation of motion of the density matrix in the presence of two fields is solved and used to analyze the response of the spin system to double irradiation under steady state. In the average frequency rotating frame, the diagonal elements of the density matrix oscillate at even harmonics of the frequency difference, while the off-diagonal elements oscillate at odd harmonics. The spectral response of the spin system can be predicted by applying the conservation rules: The frequency spectrum is a consequence of the conservation of total angular momentum, while the resonance condition is the result of the conservation of energy. The interpretive and predictive nature of the theoretical framework presented is illustrated by the treatment of the classical Anderson experiment and the simulation of the splitting of the multiquantum signal at high frequency difference. Approximate expressions for the population differences and coherences are derived and graphic representation is used to study the general nonlinear dependence on spectral parameters. At low values of the saturation parameter S, the n-quantum absorption is proportional to dT2S(n-1)/2 where d = 1/2gammaH. Therefore, the signal amplitude is proportional not only to T2, but also to powers of T1T2, which makes the multiquantum signals more sensitive to relaxation rates than conventional one-photon displays. The frequency difference swept line shape of the multiquantum signal depends on both T1 and T2. However, when T2 much less than T1, the new spectroscopic dimension, namely, the frequency difference, can be used to determine the spin-lattice relaxation time. Several spectroscopic features of multiquantum signals are discussed in the context of the general mathematical equivalence of double irradiation and amplitude modulation spectroscopy.