Manipulation of atoms by optical field

If a super-cooled atomic gas is placed in a standing light wave produced by two counter-propagating lasers of certain frequency, the atoms are diffracted in different order. A cold atom absorbs a photon from one of the laser beams and emits a photon in the other beam receiving a net momentum of ${\displaystyle 2\hbar k}$ in the direction of the absorbed photon. Here ${\displaystyle k}$ is the magnitude of the wave vector of the laser. This is called two-photon recoil process. In such situation, a BEC cloud sitting at the center of a trap is split into two identical clouds. The clouds then travel in opposite directions with a velocity, ${\displaystyle v=2\hbar k/m}$ in the direction of the photon.