I have a couple of questions regarding laser cooling. I should preface this by saying that I've taken a course in Modern Physics, so I don't have more than a very basic understanding of QM. In this case, I am familiar with absorption/emission lines, Zeeman effect, degeneracy and quantum numbers, and the Doppler shift at the elementary level. 1) I am confused about how a magnetic field can precisely be responsible for the continued slowing of atoms. I've read that essentially the decrease in the Doppler shift is compensated for by a decrease in the Zeeman effect. So it seems after initially interacting with the laser, the atom slows down and "sees" a smaller frequency, but as the B-field is weaker, it actually will absorb this lower frequency because the new transition is smaller. But is the Zeeman shift exactly compensate the Doppler shift, so that as the atom moves down the axis the experimenter will not need to change the laser frequency? That these two factors would cancel each other out exactly seems unlikely/remarkable to me. And if that isn't it, what really is the advantage to using the magnetic field? As a concrete example, would it be fair to say this: An atom is in the ground state, interacts with the laser in a magnetic field, and then may have the energy state defined by n,l,m=1,1,1 (for ex.); it then re-emits the photon in a random direction and goes back to the ground state. As it proceeds through more slowly, it continues to absorb and emit. Is that correct? 2) Are these atoms bouncing back and forth on the walls until they gradually slow down, or will the atoms grind to a (near) halt all in one pass? 3) How exactly is polarization of laser light related to the Zeeman Effect? I am confused as to why this happens. Thanks for reading and I appreciate any help with this!