Atom optics with magnetic surfaces .2. Microscopic analysis of the 'floppy disk' mirror

In a recent experiment we studied cold rubidium atoms bouncing on a magnetic mirror made from a flexible computer disk with sinusoidal magnetization. The motion was well described by a model in which the mirror was a perfect specular reflector, but complete agreement with the data required the reflecting surface to be slightly corrugated. Here we explore the physical origins of the corrugation both theoretically and experimentally. First, we develop a theory relating the reflecting force on the atoms to the magnetization of the mirror, taking into account the finite thickness of the magnetic film. We find that if the signal on the floppy disk is not harmonic the atoms appear to have been reflected from a corrugated surface, as observed in our recent experiment. Next, we describe magnetic force microscope measurements which allow us to determine the distortion on the disk and hence to quantify its effect on the reflected atoms. We show that recording nonlinearity is indeed a major cause of the mirror roughness. We also consider other sources of roughness and identify an important effect associated with the boundaries between recorded tracks. Agreement between our experiment and theory suggests that we have identified the limiting factors in a real atom-optical element made from a floppy disk. At present the angular resolution of the mirror is approximately 35 mrad for atoms dropped from a height of 4 cm. We discuss how this can be improved to reach a level of 5 mrad or better.