Coherent spin-mixing and wave packets dynamics of spin-1 condensates in optical lattices

The dynamics of wave packets and spin-mixing of spin-1 condensates with repulsive spin-independent and either ferromagnetic or antiferromagnetic spin-dependent interactions in one-dimensional (1D) periodic optical lattices are discussed both analytically and numerically. In the tight-binding limit, the localized states, i.e., self-trapping, moving soliton and breather, in spin-1 condensates are obtained. The moving soliton and breather states show complex characters: if initially the condensates are prepared in spin stationary configuration, normal stable moving soliton and breather exist; however, if initially the condensates are prepared in spin non-stationary state, because of the spin-exchange process, the wave packets experience both local soliton/breather motion and larger scale periodic oscillation (with the spin-exchange period). Interestingly, we find the spin-mixing dynamics are coupled with wave packets dynamics: when the wave packets are self-trapped, the spin-mixing oscillations are also arrested to the stationary configuration; during diffusion of the wave packets, however, the spin-mixing dynamics are inhibited; a robust quasi-periodic spin-mixing oscillation maintains in moving soliton and breather states. These interesting results open up the possibility for controlled manipulation of the spin dynamics by the optical lattices.