Laser radiation force on a two-level atom

The motion of a two-level atom in a spatially inhomogeneous laser field is generally governed by the dipole gradient force, the radiation pressure force, and the diffusion of momentmn. A detailed and consistent analysis of the motion of two-level atoms in light fields can be foimd in Minogin and Letokhov (1987) and Kazantsev et al. (1990), and here I shall restrict myself to a brief amvey of the basic formulas. 

The d3Tiamics of the center of mass of an atom in a laser field are determined by the electric dipole interaction (see Section 2.4). As a result of the dipole interaction with the electric field E = E(r, t) described by the dipole interaction operator 

The energy of the dipole interaction between the atom and the laser field is 

Equation (5.6) formally coincides with the classical expression for the interaction energy of a permanent dipole with the electric field E. Accordingly, eqn (5.6) can be used directly to calculate the force F acting on an atom in a laser field E  

Equation (5.7) gives a general expression for the radiation force on an atom moving in a laser field. From a quantum mechanical point of view, the radiation force (5.7) arises as a result of the quantum mechanical momentum exchange between the atom and the laser field in the presence of spontaneous relaxation. The change in the atomic momentum comes from the elementary processes of photon absorption and emission stimulated absorption, stimulated emission, and spontaneous emission. The radiation force (5.7) is a function of the coordinates and velocity of the center of mass of the atom. 

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