An Atom Falling Toward a Wall: The Casimir-Polder Crossover From Near Field to Retarded Vacuum

An atom near a surface is attracted to it by the vacuum it shares with the surface, and the attraction changes its mathematical character at a distance the atom itself selects. This paper computes the Casimir-Polder potential for rubidium near a conducting wall in both regimes: the near field, falling as the inverse cube of the distance, and the retarded regime, falling as the inverse fourth power, joined at a crossover of 124 nanometres set by the 780-nanometre D2 transition. At a hundred nanometres the level shift is of order 0.3 megahertz, easily resolved by spectroscopy, while at two micrometres it has fallen to the kilohertz scale. These shifts are now measured routinely in atom-chip and vapour-cell experiments, making the atom-surface potential the most precisely interrogated vacuum interaction involving a single quantum object. All values are computed from stated assumptions, not measured.