Multidimensional quantum solitons with nondegenerate parametric interactions: Photonic and Bose-Einstein condensate environments - art. no. 063816

We consider the quantum theory of three fields interacting via parametric a nd repulsive quartic couplings. This can be applied to treat photonic chi(( 2)) and chi((3)) interactions, and interactions in atomic Bose-Einstein con densates or quantum Fermi gases, describing coherent molecule formation tog ether with a-wave scattering. The simplest two-particle quantum solitons or bound-state solutions of the idealized Hamiltonian, without a momentum cut off, are obtained exactly. They have a pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with a momentum cutoff. The p arametric quantum solitons have much more realistic length scales and bindi ng energies than chi((3)) quantum solitons, and the resulting effects could potentially be experimentally tested in highly nonlinear optical parametri c media or interacting matter-wave systems. N-particle quantum solitons and the ground state energy are analyzed using a variational approach. Applica tions to atomic/molecular Bose-Einstein condensates (BEC's) are given, wher e we predict the possibility of forming coupled BEC solitons in three space dimensions, and analyze "superchemistry" dynamics.