Long-distance behaviour of the surface-atom Casimir-Polder forces out of thermal equilibrium

Long-distance behaviour of the Casimir-Polder-Lifshitz force between an atom and the surface of a substrate is investigated. When the temperatures of the substrate and the environment are different, the new decay law 1/z(3) of the force at large distances is discovered, which is slower than at thermal equilibrium. The force is of a quantum nature and attractive or repulsive depending on whether the temperature of the substrate is higher or lower than that of the environment. A transparent derivation of this law is presented. It is based on a picture of evanescent waves, created in vacuum by the black-body radiation impinging on the surface near the angle of total reflection. Some new experimental possibilities of the measurement of the forces are discussed: oscillations of a Bose-Einstein condensate near the surface, Bloch oscillations of fermions in an optical lattice and phase evolution of a BEC in a double-well trap.