Analysis of a simple square magnetic lattice for ultracold atoms

We investigate the conditions under which a proposed square magnetic lattice, produced by a periodic array of square holes patterned on a magnetic film plus bias fields, can lead to magnetic microtraps with non-zero potential minima suitable for trapping periodic arrays of ultracold atoms and quantum degenerate gases. We find that the magnetic field pattern created by the array of square holes plus bias fields exhibits a complex dependence on distance z from the magnetic film, due largely to competing contributions from kz and kz decay terms (where k = 2π/a and a is the lattice period) and interference between the magnetic field pattern of the square-hole structure and the bias fields. We find that in order to avoid zero potential minima and hence losses due to Majorana spin flips, bias fields of unequal magnitude need to be applied along both the x and y (in-plane) directions plus a bias field within a specific range along the z (perpendicular) direction. We also find that for a finite-size (ns × ns) lattice, a z-bias field B1z ≈ −6M0(t/a) (where M0 and t are the film magnetization and thickness) is needed to compensate for the effect of the missing magnetic structure which would otherwise reduce the magnetic potential minima to zero