Abstract

In this paper, we discuss a permanent magnetic lattice for trapping and manipulating ultracold atoms and quantum degenerate gases. Considering three components of an external bias magnetic field, B_1x, B_1y and B_1z which are applied for controlling the magnetic lattice parameters, we obtain analytic expressions for the magnetic field minima locations as well as their absolute values, curvatures of the absolute value of the magnetic field, trap frequencies and barrier heights between minima in all directions. B_1z had previously been considered in numerical works, but not in analytic calculations, due to difficulty in obtaining the analytic expressions for the physical parameters and sufficiency of considering only B_1x and B_1y. Including the third component in this study provides further control over the magnetic lattice parameters. Also, in the presence of unavoidable bias magnetic fields with a z-component such as the Earth’s magnetic field, our analytic calculations could be useful. In numerical calculations, we have considered up to n _s  = 1001 square magnetic slabs in each direction of the 2D lattice.