Novel solitons in parametric amplifiers and atom lasers

We review recent developments in quantum and classical soliton theory, lead ing to the possibility of observing both classical and quantum parametric s olitons in higher-dimensional environments. In particular, we consider the theory of three bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical me dium this corresponds to the process of sum frequency generation (via chi(( 2)) nonlinearity) modified by the chi((3)) nonlinearity. Potential applicat ions include an ultrafast photonic AND-gate. The simplest quantum solitons or energy eigenstates (bound-state solutions) of the interacting field Hami ltonian are obtained exactly in three space dimensions. They have a point-l ike structure-even though the corresponding classical theory is nonsingular . We show that the solutions can be regularized with the imposition of a mo mentum cut-off on the nonlinear couplings. The case of three-dimensional ma tter-wave solitons in coupled atomic/molecular Bose-Einstein condensates is discussed.