Exact theory of multiphoton processes and four-photon squeezed states via nonlinear canonical transformations
Silvio De Siena, Antonio Di Lisi, Fabrizio Illuminati · Journal of Physics B Atomic Molecular and Optical Physics · 2002
We introduce nonlinear canonical transformations that yield effective, solvable 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 behaviour 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.