Impact of dispersion forces on matter-wave scattering near a dielectric disk
AbstractThe influence of the Casimir-Polder potential upon matter-wave scattering near a dielectric disk is considered. We employ a rescaled Dyson series in order to take into account the disk geometry, and compare this with a previously used approach based on the proximity-force approximation. In the latter approach one uses a simplified potential that is sharply switched on in the region of the disk. This intrinsically neglects edge and saturation effects. We show that under appropriate conditions the previous simpler model works very well for the calculation of the phase accumulated along the full path of the particle due to approximate cancellations of the errors. We present specific results for experimentally relevant scenarios, namely indium atoms or deuterium molecules interacting with a silicon nitride or silicon dioxide disk. Finally we compare our calculations to the analytically solvable problem of an infinitely thin perfectly reflecting disk, finding the expected qualitative agreement.