Subdiffusion of Dipolar Gas in One-Dimensional Quasiperiodic Potentials

Considering the discrete nonlinear Schrödinger model with dipole-dipole interactions (DDIs), we comparatively and numerically study the effects of contact interaction, DDI and disorder on the properties of diffusion of dipolar condensate in one-dimensional quasi-periodic potentials. Due to the coupled effects of the contact interaction and the DDI, some new and interesting mechanisms are found: both the DDI and the contact interaction can destroy localization and lead to a subdiffusive growth of the second moment of the wave packet. However, compared with the contact interaction, the effect of DDI on the subdiffusion is stronger. Furthermore and interestingly, we find that when the contact interaction (λ₁) and DDI (λ₂) satisfy λ₁ ≳ 2λ₂, the property of the subdiffusion depends only on contact interaction; when λ₁ ≳ 2λ₂, the property of the subdiffusion is completely determined by DDI. Remarkably, we numerically give the critical value of disorder strength v* for different values of contact interaction and DDI. When the disorder strength v ≥ v*, the wave packet is localized. On the contrary, when the disorder strength v ≤ v*, the wave packet is subdiffusive