Magneto-optical trap

In condensed matter physics, a magneto-optical trap (MOT) is an apparatus which uses laser cooling and a spatially-varying magnetic field to create a trap which can produce samples of cold, neutral atoms. Temperatures achieved in a MOT can be as low as several microkelvin, depending on the atomic species, which is two or three times below the photon recoil limit. However, for atoms with an unresolved hyperfine structure, such as , the temperature achieved in a MOT will be higher than the Doppler cooling limit. A MOT is formed from the intersection of a weak, quadrupolar, spatially-varying magnetic field and six circularly-polarized, red-detuned, optical molasses beams. As atoms travel away from the field zero at the center of the trap (halfway between the coils), the spatially-varying Zeeman shift brings an atomic transition into resonance which gives rise to a scattering force that pushes the atoms back towards the center of the trap. This is why a MOT traps atoms, and because this force arises from photon scattering in which atoms receive momentum "kicks" in the direction opposite their motion, it also slows the atoms (i.e. cools them), on average, over repeated absorption and spontaneous emission cycles. In this way, a MOT is able to trap and cool atoms with initial velocities of hundreds of meters per second down to tens of centimeters per second (again, depending upon the atomic species). Although charged particles can be trapped using a Penning trap or a Paul trap using a combination of electric and magnetic fields, those traps are ineffective for neutral atoms. Two coils in an anti-Helmholtz configuration are used to generate a weak quadrupolar magnetic field; here, we will consider the coils as being separated along the -axis. In the proximity of the field zero, located halfway between the two coils along the -direction, the field gradient is uniform and the field itself varies linearly with position. For this discussion, consider an atom with ground and excited states with and , respectively, where is the magnitude of the total angular momentum vector.

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