Hi Carnot, I know this response is coming in a bit late, but better late than never..
TOP traps are useful for making Bose-Einstein Condensates with alkali atoms. Normally you start with a magneto-optical trap (MOT) and then evaporate the atoms for the next stage in cooling. MOT's generally use a quadrupole trap which is made from two current-carrying coils with the the fields anti-aligned (anti-Helmholtz configuration). The atoms are held in the magnetic trap if they are in a low-field seeking state. Evaporation is carried out using radio frequency waves which force atoms at a certain part of the field (based on their Zeeman splitting) into a high-field seeking state and thus ejecting them from the trap. The problem with _just_ using a quadrupole trap is that when the atoms pass through the zero-point in the magnetic field they no longer have a well defined quantization axis and can undergo a Majorana spin-flip. This puts the atoms in a high field seeking state causing them to be lost from the trap.
The solution to plugging the "hole" in the center of the quadrupole trap has been solved several different ways by now, but the TOP trap was the solution which allowed for the first experimental realization of BEC. If you think of the axis of the quadrupole coils as the z axis, then the TOP trap is made of 4 coils with 2 along the x axis and 2 along the y axis. Each coil pair generates a homogeneous bias field (Helmholtz configuration) which can be directed along x or -x (and y or -y for the other pair). By feeding the coils along the x axis a sinusoidal current and an identical current which is 90 degrees out of phase along the y axis coils, you can create a bias field which simply rotates over time.
If you imagine the bias field turning on quickly, the quadrupole field is displaced causing the field zero to move away from the atoms. The atoms will slowly roll down the potential back toward the zero point in the quadrupole field. However, the TOP field rotates and moves the zero point to a different location before the atoms can catch up. The rotating field pushes the zero around the cloud at some radius (which is determined by the bias field strength), and the rotation rate is fast enough that the atoms can never catch up. The resulting potential shape is calculated by averaging the displaced quadrupole field at each point in the TOP phase. Upon taking the average of the field, the minimum potential in the trap is no longer at a point where the magnetic field amplitude is zero. This setup only allows Majorana spin flips if the amplitude of the bias field is reduced such that the zero point in the field is passing through the atomic cloud. The circle that the zero point traces out can be used to evaporate atoms and is commonly referred to as the "circle of death".