Stability analysis of three-dimensional breather solitons in a Bose-Einstein Condensate
arXiv:cond-mat/0506534 · doi:10.1098/rspa.2005.1531
Abstract
We investigate the stability properties of breather soliton trains in a three-dimensional Bose-Einstein Condensate with Feshbach Resonance Management of the scattering length. This is done so as to generate both attractive and repulsive interaction. The condensate is con ned only by a one dimensional optical lattice and we consider both strong, moderate, and weak con nement. By strong con nement we mean a situation in which a quasi two dimensional soliton is created. Moderate con nement admits a fully three dimensional soliton. Weak con nement allows individual solitons to interact. Stability properties are investigated by several theoretical methods such as a variational analysis, treatment of motion in e ective potential wells, and collapse dynamics. Armed with all the information forthcoming from these methods, we then undertake a numerical calculation. Our theoretical predictions are fully con rmed, perhaps to a higher degree than expected. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi two-dimensional treatment, when the dynamics in one direction are frozen. We nd that in the 3D case the stability region splits into two parts. However, as we tighten the con nement, one of the islands of stability moves toward higher frequencies and the lower frequency region becomes more and more like that for quasi 2D. We demonstrate these solutions in direct numerical simulations and, importantly, suggest a way of creating robust 3D solitons in experiments in a Bose Einstein Condensate in a one-dimensional lattice.
arXiv comment14 pages, 6 figures; accepted to Proc. Roy. Soc. London A
References in corpus (16)
- Formation and Propagation of Matter Wave Soliton Trains
- Formation of a Matter-Wave Bright Soliton
- Dark Solitons in Bose-Einstein Condensates
- Realization of Bose-Einstein condensates in lower dimensions
- Dynamics of collapsing and exploding Bose-Einstein condensates
- Bright gap solitons of atoms with repulsive interaction
- Tuning the scattering length with an optically induced Feshbach resonance
- Influence of nearly resonant light on the scattering length in low-temperature atomic gases
- Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate
- Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
- Multidimensional solitons in periodic potentials
- Stabilization of solitons of the multidimensional nonlinear Schrodinger equation: Matter-wave breathers
- Mean-field analysis of collapsing and exploding Bose-Einstein condensates
- Stabilization of three-dimensional matter-waves solitons in an optical lattice
- Bose-Einstein droplet in free space
- An all-optical gray lattice for atoms