Mechanical force in laser cooling and trapping

Laser cooling and trapping are based on the mechanical force an electromagnetic wave (EMW) exerts upon an atom. The force is generally explained as the result of the conservation law of the linear momentum of a photon and the atom. In contrast, we have directly derived the force from primary electromagnetism in order to clarify its origin. We regarded the atom as an electric dipole moment induced by the EMW, and examined the interaction between the dipole moment and the EMW. We applied a semiclassical theory in which the atom is quantized as a two-level system but the electromagnetic field is not; no photon is introduced. The results are consistent with the commonly accepted explanation, and explicitly demonstrate the contribution of the electric and magnetic fields to the force, in particular, the significance of the longitudinal magnetic field for the dipole force in laser trapping.