Thermal spin flips in atom chips

We derive a general expression for the spin-flip rate of an atom trapped near an arbitrary dielectric body and we apply this theory to the case of a two-layer cylindrical metal wire. The spin-flip lifetimes we calculate are compared with those expected for an atom near a metallic slab and with those measured by Jones above a two-layer wire [ M.P.A. Jones, C.J. Vale, D. Sahagun, B.V. Hall, and E.A. Hinds, Phys. Rev. Lett. 91, 080401 (2003) ]. We investigate how the lifetime depends on the skin depth of the material and on the scaling of the dimensions. This leads us to some conclusions about the design of integrated circuits for manipulating ultracold atoms (atom chips).