An Effective-Mass Theory for Bright Gap Solitons in Optical Lattices

Szu-Cheng Cheng

Chinese Journal of Physics

43卷4期（2005 / 08 / 01）

835 - 846

英文

A one-band effective-mass (EFM) theory was developed to study the properties of the localized states of a Bose-Einstein condensate (BEC) in a periodic optical potential with either attractive or repulsive atom interactions. The localized states of the BEC are solitons in the gaps or gap solitons. The analytic solutions of the gap solitons are a Bloch function from periodicity, modulated by a soliton envelope function of the nonlinear Schrödinger equation. The soliton width is determined by the detuning chemical potential from the band edge. The detuning chemical potential in the nonlinear Schrödinger equation indicates that not all the atoms in the condensate are used for forming gap solitons, and that some atoms form the background of nonlinear modes. The background atoms are determined by the chemical potential at the band edge. The gap solitons form on top of the background atoms.