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Magnetic traps for cold atoms have become a powerful tool of cold atomphysics and condense matter research. The traps on superconducting chips allowone to increase the trapped atom life- and coherence time by decreasing thethermal noise by several orders of magnitude compared to that of the typicalnormal-metal conductors. A thin superconducting film in the mixed state is,usually, the main element of such a chip.  Using a finite element method to analyze thin film magnetization andtransport current in type-II superconductivity, we study magnetic trapsrecently employed in experiments. The proposed approach allows us to predictimportant characteristics of the magnetic traps (their depth, shape, distancefrom the chip surface, etc.) necessary when designing magnetic traps in coldatom experiments.

3D modeling of magnetic atom traps on type-II superconductor chips