We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.

我们研究了深一维光学晶格中偶极玻色-爱因斯坦凝聚体的稳定特性，并具有额外的外部参数调制谐波陷阱势。通过解析和数值方法，我们求解了具有短程接触相互作用和长程偶极-偶极相互作用的无量纲非局部非线性离散 Gross-Pitaevskii 方程。结果表明，调制深光学晶格中偶极凝聚体的稳定性可以通过接触相互作用、偶极相互作用和外部调制的耦合效应来控制。当偶极相互作用、接触相互作用、平均电位强度和调制的幅频比满足临界条件时，系统可以稳定。另外，呼吸状态，预测了扩散状态和吸引相互作用诱导的陷阱状态。晶格的偶极相互作用和外部调制在稳定凝聚物中起重要作用。