Trilayer permanent magnetic lattice for ultracold atoms formed by two square-hole magnetic layers

We propose and analyze a trilayer permanent magnetic lattice formed by two patterned magnetic films, each containing a two-dimensional array of square holes, generating three distinct two-dimensional arrays of three-dimensional microtraps with nonzero minima, thereby suppressing Majorana spin-flip losses. Analytical expressions for key trapping parameters are derived and show good agreement with numerical calculations. A bias magnetic field enables tunable control of trap frequencies, depths, and modulation amplitudes. We find that the interlayer region supports higher trap frequencies than the outer layers, and that the confinement properties depend sensitively on the separation distance between the films. The trilayer architecture enables vertical confinement engineering, allowing precise three-dimensional positioning of traps and independent control of trap curvatures in the central and outer regions, including the formation of an interlayer potential with enhanced confinement. Owing to its stability, low decoherence, and experimental feasibility, the proposed lattice provides a promising platform for the manipulation of ultracold atoms and potential applications in quantum information processing.