Surface roughness contribution to the Casimir interaction between an isolated atom and a cavity wall

An approximate perturbative method is developed to calculate the corrections to the Casimir force between an isolated atom and a cavity wall due to surface roughness. The results are obtained up to the fourth order in the relative roughness amplitude. All possible types of surface roughness are considered: large scale, short scale, and intermediate, defined by the ratio of the characteristic lateral length scale of roughness to the atom-wall distance. A continuous transition between the corrections due to different types of roughness is carried out. It is shown that the large-scale roughness can lead to corrections of the order of 70% of the net Casimir force. In the cases of large-scale and intermediate-type roughness the lateral Casimir force comes into play, which leads to moving the atom to the nearest extreme point of the vertical force with subsequent dying out oscillations in its vicinity. Possible role wall roughness can play in some phenomena of cavity electrodynamics is discussed.