We describe the finite-element modeling and fabrication of chip-based superconducting traps for levitating micrometer-sized superconducting particles. Such experiments promise to lead to a new generation of macroscopic quantum experiments and of force and acceleration sensors. An accurate modeling of the utilized trap architectures is crucial for predicting parameters of the traps, such as trap stability, frequency and levitation height, in realistic situations accounting for the finite extent of the involved superconducting objects. To this end, we apply a modeling method that is applicable to arbitrary superconducting structures in the Meissner state. It is based on Maxwell-London equations in the static regime using the A-V formulation. The modeling allows us to simulate superconducting objects with arbitrary geometry subject to arbitrary magnetic field distributions and captures finite volume effects like magnetic field expulsion. We use this modeling to simulate two chip-based trap architectures: an anti-Helmholtz coil-type trap and a planar double-loop trap. We calculate important parameters of the superconducting traps for the cases of levitating micrometer-sized particles of either spherical, cylindrical or ring shape. We compare our modeling results to analytical test cases for idealized geometries. We also model detection of the motion of the levitated particle by measurement of flux-changes induced in a nearby pick-up loop. We demonstrate the fabrication of the analyzed chip-based traps and particles using thin Nb films. Our modeling is generic and has applications beyond the one considered, such as designing superconducting magnetic shields or for calculating filling factors in superconducting resonators.

中文翻译：

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用于悬浮微米级超导粒子的基于芯片的超导陷阱

我们描述了用于悬浮微米级超导粒子的基于芯片的超导陷阱的有限元建模和制造。这样的实验有望导致新一代宏观量子实验以及力和加速度传感器。在考虑到所涉及超导物体的有限范围的现实情况下，所用陷阱结构的准确建模对于预测陷阱的参数（例如陷阱稳定性、频率和悬浮高度）至关重要。为此，我们应用了一种适用于迈斯纳态的任意超导结构的建模方法。它基于静态状态下的 Maxwell-London 方程，使用 AV 公式。该建模使我们能够模拟具有任意几何形状的超导物体，受任意磁场分布的影响，并捕获有限体积效应，如磁场驱逐。我们使用此建模来模拟两种基于芯片的陷阱架构：反亥姆霍兹线圈型陷阱和平面双回路陷阱。对于悬浮球形、圆柱形或环形的微米级粒子，我们计算了超导陷阱的重要参数。我们将我们的建模结果与理想化几何的分析测试用例进行比较。我们还通过测量附近拾取回路中引起的通量变化来模拟悬浮粒子运动的检测。我们展示了使用 Nb 薄膜制造分析的基于芯片的陷阱和粒子。