  A perturbative analytic operator solution of a completely quantum mechanical
Hamiltonian of multi-photon pump non-degenerate hyper-Raman process is
obtained. It is shown that the obtained solution is general in nature as the
solutions of non-degenerate hyper-Raman and stimulated Raman processes can be
obtained as special cases of the present solution. The analytic solutions
obtained here are used to investigate the nonclassical properties of the
different modes in the stimulated, spontaneous and partially spontaneous
multi-photon pump non-degenerate hyper-Raman processes. The nonclassical nature
of these processes is witnessed by means of single mode and intermodal
quadrature squeezing, intermodal entanglement of different orders, lower order
and higher order photon antibunching. Interestingly, manifesting the
multiphoton nature of the pump modes, a bunch of nonclassicality involving them
are observed due to self-interaction of various pump modes.
