  We introduce nonlinear canonical transformations that yield effective
Hamiltonians of multiphoton down conversion processes, and we define the
associated non-Gaussian multiphoton squeezed states as the coherent states of
the multiphoton Hamiltonians. We study in detail the four-photon processes and
the associated non-Gaussian four-photon squeezed states. The realization of
squeezing, the behavior of the field statistics, and the structure of the phase
space distributions show that these states realize a natural four-photon
generalization of the two-photon squeezed states.
