  Interaction of intense laser beam with an inversion symmetric third order
nonlinear medium is modeled as a quartic anharmonic oscillator. A first order
operator solution of the model Hamiltonian is used to study the possibilities
of generation of higher order nonclassical states. It is found that the higher
order squeezed and higher order antibunched states can be produced by this
interaction. It is also shown that the higher order nonclassical states may
appear separately, i.e. a higher order antibunched state is not essentially
higher order squeezed state and vice versa.
