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本文探讨了莫尔晶格扭转角对玻色-爱因斯坦凝聚体中带隙孤子的调控作用. 结果表明, 扭转角度明显影响莫尔晶格的周期和系统的线性能带结构, 对带隙孤子的结构及稳定性有着重要影响. 在半无限带隙(吸引作用主导), 势阱深度越深, 孤子密度越大. 而在第一带隙(排斥作用主导), 孤子密度随势阱深度呈现相反变化规律. 线性稳定性分析和非线性动力学演化表明, 第一带隙内找到的孤子普遍稳定; 而在半无限带隙中, 孤子稳定性与其类型及空间构型密切相关: 单峰孤子, 峰间距大的多峰孤子及峰间距近的异相孤子较为稳定, 而同相多峰孤子则易失稳. 研究同时发现, 越靠近能带边缘, 孤子的稳定性越好. 该研究为调控莫尔超晶格中的非线性孤子提供了理论依据.This study investigates gap solitons and their stability in Bose-Einstein condensates confined in Moiré optical lattices with distinct twisted angles. The results demonstrate that the twisted angle significantly modulates the Moiré periodicity and the flatness of low bands. For sufficiently large angular differences, smaller twisted angles generally lead to larger Moiré periods and flatter low bands, though this trend becomes less consistent at minimal angular differences. Moreover, smaller twisted angles yield more complex potential structures, which modify gap positions and widths, consequently affecting the properties of gap solitons. Using the Newton-conjugate gradient method, we identify various types of solitons in Moiré lattice with four different twisted angles, observing that solitons can exist over a broader range of potential depths at smaller twisted angles. The density distributions of solitons exhibit markedly different behaviors in different gaps: in the semi-infinite gap dominated by attractive interactions, deeper potentials lead to reduced soliton density, whereas in the first gap governed by repulsive interactions, deeper potentials enhance soliton density distributions. Linear stability analysis and nonlinear dynamical evolution results indicate that solitons found in the first gap(including both single-humped and multi-humped structures) demonstrate robust dynamical stability, whereas in the semi-infinite gap, single-humped solitons maintain good stability, while closely separated multi-humped in-phase solitons tend to be unstable, with enhanced stability observed for solitons located closer to the band edges. This work provides a theoretical foundation for manipulating nonlinear solitons in Moiré superlattices.
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Keywords:
- Moiré optical lattice /
- Bose-Einstein condensate /
- gap soliton /
- twisted angle
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