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

TL;DR

This paper theoretically analyzes 3D matter-wave solitons in coupled atomic-molecular Bose-Einstein condensates, exploring their stability and potential for experimental realization, extending previous optical soliton models to quantum gases with complex nonlinear interactions.

Contribution

It introduces an approximate analytical approach to 3D solitons in coupled BECs, including stability analysis considering higher-order nonlinear effects and atom-molecule interactions.

Findings

Stable 3D solitons are predicted under certain parameters.

Numerical simulations confirm the stability of solitons in 3D lattice models.

The work suggests a method to demonstrate ground states of non-local BEC equations.

Abstract

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.