MOT How To

From Qwiki

Here is a recipe for building a Magneto-Optic Trap (MOT) for cold Alkali atoms. You need three things:

Magnetic System: A set of anti-Helmholtz coils to provide the appropriate magnetic field gradient.
Optical System: The appropriate trapping and cooling light.
Vacuum System: A gas of alkali atoms in an otherwise evacuated vacuum chamber.

1 Magnetic System
2 Laser System
3 Optical System
4 Vacuum System
5 Miscellany
6 References
7 Further Directions

Magnetic System

As everyone knows from their Griffiths problem sets, the Helmholtz coil is a lovely way of generating a particularly uniform magnetic field. Two coils separated by a distance $d\,$ equal (or nearly so) to the radius $r\,$ will generate a field whose first and second derivatives along the preferred direction vanish at the center point.

This is all well and good, but for a MOT we're more interested in creating a locally uniform field gradient in order to provide the spatially dependent Zeeman shift that makes a MOT a trapping system rather than just a cooling one. To do this, one simply reverses the current in one arm of the Helmholtz coil, and voila, an anti-Helmholtz coil springs into being, fully formed.

If one is interested in particularly uniform gradients, there is an anti-Helmoltz condition similar to the Helmholtz relation $d=r\,$ ; a little noodling reveals that if $d=\sqrt{3}r\,$ , the gradient's derivative vanishes at the origin.

Most MOT-coil calculations are done off-the-cuff along the center-line; this is because of the fact that the transverse field gradients are always a factor of two smaller than the z-gradient regardless of the ratio $d/r\,$ , a fact that is useful to carry in the back of one's mind.

It should be noted that in the z-direction, at least, many higher derivatives also vanish when the special conditions are met, but this is of vanishingly small practical use. In fact, the whole notion of matching the special condition is rarely, if ever, thought about in the laboratory when constructing a MOT; one goes with the tightest geometry that one has in order to get the most $B^\prime$ oomph out of the current supply on one's rack, within reason. Gradient nonuniformities shouldn't really be on a worry-list unless you're making the Viscount of MOTs.