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Chinese Physics Letters

Dynamical Stability of Gap Soliton of One-Dimensional Condensate in Optical Lattices with Strong Interatomic Interaction

Denglong Wang, Xiaohong Yan, Fengjiao Wang

Published Jun 28, 2007• 22 citations
Publisher

Abstract

By developing the multiple scales method, we analytically study the dynamics properties of gap soliton of Bose–Einstein condensate in optical lattices. It is shown that the gap soliton will appear at Brillouin zone edge of linear band spectrum of the condensates when the interatomic interaction strength is larger than the lattice depth. Moreover, the density of gap soliton starts to be relatively small, while it increases with time and becomes stable.

DOI
10.1088/0256-307x/24/7/009

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By developing the multiple scales method, we analytically study the dynamics properties of gap soliton of Bose–Einstein condensate in optical lattices. It is shown that the gap soliton will appear at Brillouin zone edge of linear band spectrum of the condensates when the interatomic interaction strength is larger than the lattice depth. Moreover, the density of gap soliton starts to be relatively small, while it increases with time and becomes stable.
We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose–Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose–Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose–Einstein condensate.
By developing a multiple-scale method, we study analytically the dynamics of the soliton inside the semi-infinite band gap (SIBG) of quasi-one-dimensional Bose–Einstein condensates trapped in an optical lattice. In the linear case, a stable condition of soliton formation is obtained. For a weak nonlinearity, whether there occurs a spatially propagating or localized gap soliton is determined by the lattice depth. Meanwhile, we predict the existence of the dark (bright) gap solitons for the repulsive (attractive) interactions in the SIBG, different from that of the gap solitons in other energy gaps. And the collision of two dark (or bright) solitons is nearly elastic under a safe range of atomic numbers. An experimental protocol is further designed for observing these phenomena.
We study the gap solitons and nonlinear Bloch waves of interacting bosons in one-dimensional optical lattices, taking into account the interaction from the weak to the strong limits. It is shown that composition relation between the gap solitons and nonlinear Bloch waves exists for the whole span of the interaction strength. The linear stability analysis indicates that the gap solitons are stable when their energies are near the bottom of the linear Bloch band gap. By increasing the interaction strength, the stable gap solitons can become unstable. It is argued that the stable gap solitons can easily be formed in a weakly interacting system with energies near the bottom of the lower-level linear Bloch band gaps.
We analyze the dynamical stability of gap solitons formed in a quasi-one-dimensional Bose-Einstein condensate in an optical lattice. Using two different numerical methods we show that, under realistic assumptions for experimental parameters, a gap soliton is stable only in a truly one-dimensional situation. In two and three dimensions, resonant transverse excitations lead to dynamical instability. The time scale of the decay is numerically calculated and shown to be large compared to the characteristic time scale of solitons for realistic physical parameters.
Energy band structure and stability of Bose-Einstein condensate with both two- and three-body interactions in one-dimensional periodic optical lattices are discussed. It is demonstrated that the lowest energy band can show a loop structure at the boundary of the first Brillouin zone only when the number of atoms is larger than a critical value. When the loop structure is excited, an analytical expression of the loop width is obtained. The energetical and dynamical stabilities of the system are determined by considering the behavior of the Gross-Pitaevskii energy functional when the condensate wave function diverge away from a stationary state upon small perturbation, and its dependence on the number of atoms, the magnitude of the periodic potential, especially, the strength of the three-body force are studied. In addition, a criteria of the stability for excitations with long wavelengths is given by applying the hydrodynamic approach. The influence of the three-body interaction on the band properties and the stabilities are discussed in detail. It is shown that the critical density for developing the loop structure, the loop width, and the instability criteria are modified dramatically by the three-body interaction.