Three-dimensional solitons in coupled atomic-molecular Bose-Einstein condensates

Details Three-dimensional solitons in coupled atomic-molecular Bose-Einstein condensates Three-dimensional solitons in coupled atomic-molecular Bose-Einstein condensates

2004-10-10

arxiv.org/abs/cond-mat/0410234v2

Phys. Rev. A 70, 063611 (2004)

Physics

Condensed Matter

Other Condensed Matter

Final published version (minor modifications to the text)

Scientific paper

10.1103/PhysRevA.70.063611

We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BEC). The soliton solutions to the mean-field equations are obtained in an approximate analytical form by means of a variational approach. We investigate soliton stability within the parameter space described by the atom-molecule conversion coupling, atom-atom s-wave scattering, and the bare formation energy of the molecular species. In terms of ordinary optics, this is analogous to the process of sub/second-harmonic generation in a quadratic non-linear medium modified by a cubic nonlinearity, together with a phase mismatch term between the fields. While the possibility of formation of multidimensional spatio-temporal solitons in pure quadratic media has been theoretically demonstrated previously, here we extend this prediction to matter-wave interactions in BEC systems where higher-order non-linear processes due to interparticle collisions are unavoidable and may not be neglected. The stability of the solitons predicted for repulsive atom-atom interactions is investigated by direct numerical simulations of the equations of motion in a full 3D lattice. Our analysis also leads to a possible technique for demonstrating the ground state of the Schroedinger-Newton and related equations that describe Bose-Einstein condensates with non-local inter-particle forces.

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