具有光晶格的玻色-爱因斯坦凝聚体中的隙型暗局域模
Gap-type dark localized modes in a Bose-Einstein condensate with optical lattices
摘要：
玻色-爱因斯坦凝聚体（BEC）表现出许多令人惊奇的宏观现象，近年来引起了人们的广泛关注，特别是在孤子及其相关的非线性现象方面。同时，光晶格已经成为理解BEC性质和控制BEC动力学的通用工具箱，其中亮隙孤子的实现是一个标志性的结果。然而，暗隙孤子仍然是未经实验证实的，并且它们在多个维度上的性质仍然未知。基于此，我们从理论和数值上研究了超冷原子在光晶格中的隙型暗局域模的形成和稳定性。在一维和二维的几何结构中，我们预测了两种稳定的暗局域模--带隙孤子和孤子团。这两种模式的涡旋对应物也被构造在二维中。一个独特的特点是存在一个非线性布洛赫波背景上的所有上述间隙模式位于。采用线性稳定性分析和直接模拟，预测模式的稳定区域。我们的研究结果提供了在超冷原子实验及其他领域，包括在光子晶体和晶格光学中，用尖端技术观察暗隙局域结构的可能性。
英文摘要：
Bose-Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years--particularly in the field of solitons and associated nonlinear phenomena. Meanwhile, optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC, among which the realization of bright gap solitons is an iconic result. However, the dark gap solitons are still experimentally unproven, and their properties in more than one dimension remain unknown. In light of this, we describe, numerically and theoretically, the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices. Two kinds of stable dark localized modes--gap solitons and soliton clusters--are predicted in both the one- and two-dimensional geometries. The vortical counterparts of both modes are also constructed in two dimensions. A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated. By employing linear-stability analysis and direct simulations, stability regions of the predicted modes are obtained. Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond, including in optics with photonic crystals and lattices.
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