Radiofrequency (RF) induced evaporative cooling is the most common method for evaporatively cooling atoms in a magneto-optical trap (MOT). Consider trapped atoms laser cooled on a |F=0⟩ → |F=1⟩ transition. The magnetic sublevels of the |F=1⟩ state (|m F = -1,0,1⟩) are degenerate for zero external field. The confining magnetic quadrupole field, which is zero at the center of the trap and nonzero everywhere else, causes a Zeeman shift in atoms which stray from the trap center, lifting the degeneracy of the three magnetic sublevels. The interaction energy between the total spin angular momentum of the trapped atom and the external magnetic field depends on the projection of the spin angular momentum onto the z-axis, and is proportional to Δ Δ E ∝ ∝ − − m F B Z From this relation it can be seen that only the |m F =-1⟩ magnetic sublevel will have a positive interaction energy with the field, that is to say, the energy of atoms in this state increases as they migrate from the trap center, making the trap center a point of minimum energy, the definition of a trap. Conversely, the energy of the |m F =0⟩ state is unchanged by the field (no trapping), and the |m F =1⟩ state actually decreases in energy as it strays from the trap center, making the center a point of maximum energy. For this reason |m F =-1⟩ is referred to as the trapping state, and |m F =0,1⟩ the non-trapping states. From the equation for the magnetic field interaction energy, it can also be seen that the energies of the |m F =1,-1⟩ states shift in opposite directions, changing the total energy difference between these two states. The |m F =-1⟩→|m F =1⟩ transition frequency therefore experiences a Zeeman shift. With this in mind, the RF evaporative cooling scheme works as follows: the size of the Zeeman shift of the -1→+1 transition depends on the strength of the magnetic field, which increases radially outward from the trap center. Those atoms which are coldest move within a small region around the trap center, where they experience only a small Zeeman shift in the -1→+1 transition frequency. Warm atoms, however, spend time in regions of the trap much further from the center, where the magnetic field is stronger and the Zeeman shift therefore larger. The shift induced by magnetic fields on the scale used in typical MOTs is on the order of MHz, so that a radiofrequency source can be used to drive the -1→+1 transition. The choice of frequency for the RF source corresponds to a point on the trapping potential curve at which atoms experience a Zeeman shift equal to the frequency of the RF source, which then drives the atoms to the anti-trapping |m F =1⟩ magnetic sublevel and immediately exits the trap. Lowering the RF frequency is therefore equivalent to lowering the dashed line in the figure, effectively reducing the depth of the potential well. For this reason the RF source used to remove these energetic atoms is often referred to as an "RF knife," as it effectively lowers the height of the trapping potential to remove the most energetic atoms from the trap, "cutting" away the high energy tail of the trap's energy distribution. This method was famously used to cool a cloud of rubidium atoms below the condensation critical temperature to form the first experimentally observed Bose-Einstein condensate (BEC) .