Matter and field spectral densities for multidimensional optical response

In the semiclassical theory of multidimensional spectroscopy, which describes a classical field coupled to quantum matter, n-th order signals are calculated as a convolution of n spectral field envelopes and an n-th order matter response function which enforces the time-ordering of interactions. In quantum field spectroscopy, the electromagnetic field is in a nonclassical state and the product of spectral field envelopes is replaced by a correlation function of the associated field operators. In this paper, we introduce a complementary representation in which the roles of field and matter are interchanged and signals are given by an ordinary, correlation function of matter convoluted with a time-ordered response function of the field. This suggests an inverse spectroscopy which uses matter to probe the state of the field.