Multidimensional spectroscopy

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Abstract
The quantum states produced by non-linear interaction of a coherent uniform radiation field with dipolar matter are evaluated by a time-dependent perturbation expansion of the density matrix. The non-linear terms of the expansion are Fourier transformed to yield multi-dimensional spectra which indicate the connectivities in the underlying energy level diagrams. The spectra can be measured in experiments with multiple resonance, multiple pulse or stochastic excitation. Although the theory presented is of general validity in coherent spectroscopy, emphasis is placed on its application in non-linear N.M.R. spectroscopy. It illustrates particularly well the common basis of double, 2D correlated and multi-dimensional stochastic magnetic resonance.