To answer this question, we must first answer the question "What effect does a magnetic field have on atoms?" The short answer is "It depends." The response of an atom to a magnetic field depends on the atom's magnetic dipole moment. The magnetic dipole moment is a vector quantity that tells you how strongly the object will try to rotate and align itself with an externally applied magnetic field, and any object that creates magnetic fields has an associated magnetic dipole moment. Think of a bar magnet with a North and South Pole. If you try to touch this magnet with another one that is aligned in the opposite direction (i.e. aligned like N-S S-N), then the second magnet will resist and try very hard to rotate and align itself with the field of the first magnet. But if we instead bring a wood block up to the first magnet, it won't resist us touching the other magnet at all. This is due to the magnet having a vastly larger net magnetic dipole moment than a block of wood.

Protons, neutrons, and electrons, the constituent particles of atoms, also have intrinsic magnetic dipole moments, associated with the quantum mechanical spins of the particles. The total magnetic moment of an atom is the vector sum of these constituent magnetic moments. The key point for MOTs is that an atom with a nonzero total magnetic moment will have quantum states that increase in energy with increasing magnetic field and states that decrease in energy, depending on the orientation of the atom's magnetic moment with the external magnetic field of the MOT [2]. This property of atoms with magnetic moments is called the Zeeman effect, and is depicted in Figure 2 below.