Improved Effective Range Expansion for Casimir-Polder potential

We study the effective range expansion of scattering on a real Casimir-Polder potential. We use Liouville transformations which transform the potential landscape while preserving the reflection and transmission amplitudes. We decompose the scattering calculation in two more elementary problems, one for the homogeneous 1/z^4 potential and the other one for the correction to this idealization. We use the symmetries of the transformed problem and the properties of the scattering matrices to derive an improved effective range expansion leading to a more accurate expansion of scattering amplitudes at low energy

Fluctuations of the Casimir potential above a disordered medium

We study the statistical fluctuations of the Casimir potential felt by an atom approaching a dielectric disordered medium. Starting from a microscopic model for the disorder, we calculate the variance of potential fluctuations in the limit of a weak density of heterogeneities. We show that fluctuations are essentially governed by scattering of the radiation on a single heterogeneity, and discuss in which limits they become larger than the average value predicted by effective medium theory. Finally, for denser disorder we show that multiple scattering processes become relevant.Comment: 9 pages, 5 figure

Statistical approach to Casimir-Polder potentials in heterogeneous media

We explore the statistical properties of the Casimir-Polder potential between a dielectric sphere and a three-dimensional heterogeneous medium, by means of extensive numerical simulations based on the scattering theory of Casimir forces. The simulations allow us to confirm recent predictions for the mean and standard deviation of the Casimir potential, and give us access to its full distribution function in the limit of a dilute distribution of heterogeneities. These predictions are compared with a simple statistical model based on a pairwise summation of the individual contributions of the constituting elements of the medium.Comment: 8 pages, 8 figure

Quantum Reflection of Antihydrogen in the GBAR Experiment

In the GBAR experiment, cold antihydrogen atoms will be left to fall on an annihilation plate with the aim of measuring the gravitational acceleration of antimatter. Here, we study the quantum reflection of these antiatoms due to the Casimir-Polder potential above the plate. We give realistic estimates of the potential and quantum reflection amplitudes, taking into account the specificities of antihydrogen and the optical properties of the plate. We find that quantum reflection is enhanced for weaker potentials, for example above thin slabs, graphene and nanoporous media.Comment: Workshop on Antimatter and Gravity Bern 2013 Proceeding

The Casimir effect in the sphere-plane geometry

We present calculations of the Casimir interaction between a sphere and a plane, using a multipolar expansion of the scattering formula. This configuration enables us to study the nontrivial dependence of the Casimir force on the geometry, and its correlations with the effects of imperfect reflection and temperature. The accuracy of the Proximity Force Approximation (PFA) is assessed, and is shown to be affected by imperfect reflexion. Our analytical and numerical results at ambient temperature show a rich variety of interplays between the effects of curvature, temperature, finite conductivity, and dissipation.Comment: Proceedings of the 10th International Conference "Quantum Field Theory Under the Influence of External Conditions" (Benasque, Spain, 2011); 10 pages and 6 figure