2004/10/31 by Timothy G. Vaughan, T. G. Vaughan, K. V. Kheruntsyan +1 · 13 citations
Chemistry · Physics and Astronomy · #Atom (system on chip) #Bose–Einstein condensate #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Equations of motion #Matter wave #Nonlinear system #Optical lattice #Physics #Quadratic equation #Quantum #Quantum mechanics #Schrödinger equation #Soliton #Spectroscopy and Laser Applications #Strong Light-Matter Interactions #Superfluidity #cond-mat.other
paper · pdf · doi:10.1103/physreva.70.063611
published in Physical Review A 70(6) (American Physical Society) · Final published version (minor modifications to the text)
openalex publication_date 2004/12/14 · arxiv created 2004/12/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BECs). 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, the 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- or second-harmonic generation in a quadratic nonlinear medium modified by a cubic nonlinearity, together with a phase mismatch term between the fields. While the possibility of formation of multidimensional spatiotemporal 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 nonlinear 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 Schr"odinger-Newton and related equations that describe Bose-Einstein condensates with nonlocal interparticle forces.