Hello! I read that if we have a 2 level system (say an atom) and we make it interact with a laser whose frequency is detuned from the resonant transition frequency of the system, the atom experiences an effective potential/force. In the classical description it makes sense, but quantum mechanically I am not sure what is going on. How does the atom interacts with the laser, given that it is far detuned? I initially thought that this is due Raman stimulated emission, such that the light can excite a virtual level and make it decay by stimulated emission back to the ground state. But it seems like that violates the conservation of energy. For example if we have a photon traveling in ##+z## direction doing the excitation and the one emitted by stimulated emission goes in ##-z## (if the emitted one is in the ##+z##, the net force would be zero and we would have no effective force), for the whole atom-laser system, we are just as in the beginning (atom in the ground state and 2 quanta coherent in the field), but it seems that now the atom gained a momentum, equal to twice the momentum of the photon, and hence a kinetic energy and I am not sure where this is coming from. In Raman transition, usually we have 2 lasers either of different frequency or different power. But in all the examples I see for dipole force they use a build-up cavity with the atoms trapped at the center. But in that case we have the same power and frequency detuning, as it is basically the same laser, reflected from some mirrors and I am not sure how we get energy conservation. Can someone help me understand this? Thank you!