We analyze the existence and characteristics of discrete vortex quantum droplets with intrinsic topological charges $S$ of up to 5 in two-component Bose-Einstein condensates in a deep two-dimensional (2D) optical lattice. The 2D discrete Gross-Pitaevskii equation with a Lee-Huang-Yang (LHY) correction term is used to model the condensate, which incorporates local contact interactions and LHY corrections induced by quantum fluctuations. The characteristics of vortical modes with $S$ = 1 and $S$ = 2 are studied in detail. The chemical potential μ and peak density ${\rho }_{\max }$ of the modes are calculated as functions of the norm $N$. The $\mu -N$ curves of on-site-centered and off-site-centered modes with the same number of lattice sites are nearly identical. We make an analysis and reach a conclusion consistent with these simulation results. This system contains a nontrivial type of vortex mode known as the mixed-vortex mode, in which the two components have the same density pattern and different topological charges. To the best of our knowledge, we are the first to report vortex modes with isomorphic density patterns and heteromorphic vortices in the field of quantum droplets.

我们分析了具有固有拓扑电荷的离散涡旋量子液滴的存在和特征$\mathrm{小号}$高达 5 的双分量玻色-爱因斯坦凝聚在深二维 (2D) 光学晶格中。具有 Lee-Huang-Yang (LHY) 校正项的 2D 离散 Gross-Pitaevskii 方程用于对冷凝物进行建模，该方程结合了局部接触相互作用和由量子涨落引起的 LHY 校正。涡流模式的特点$\mathrm{小号}$ = 1 和$\mathrm{小号}$ = 2 进行了详细研究。化学势μ和峰密度${\rho }_{\mathrm{最大限度}}$模式的计算为范数的函数$ñ$. 这$\mu -ñ$具有相同晶格点数的现场中心模式和非现场中心模式的曲线几乎相同。我们进行分析并得出与这些模拟结果一致的结论。该系统包含一种非平凡类型的涡流模式，称为混合涡流模式，其中两个组件具有相同的密度模式和不同的拓扑电荷。据我们所知，我们是第一个在量子液滴领域报告具有同构密度模式和异构涡旋的涡旋模式。