When cold atoms approach a periodically magnetized surface, they are scattered by the effective repulsive potential $U(x,y)={\mu }_B{m}_{F}gB(x,y)$. If the period $a$ of the magnetized surface is larger than the de Broglie wavelength $\lambda$ of the atoms, the atoms are diffracted. We have developed a method for calculating the location and intensity of the diffraction peaks using formal scattering theory. We solve the exact two-dimensional Schrödinger equation with the finite element method and calculate the scattering amplitude $f\left(\varphi \right)$ using the integral formula; a plot of $\mid f\left(\varphi \right){\mid }^2$ provides a visualization of the diffraction pattern. By varying the experimental parameters within a realistic range, we predict the optimal conditions for observing atom diffraction.

• Received 5 October 2005

DOI:https://doi.org/10.1103/PhysRevA.73.062722