Re: [Phys-l] atomic trap question

[John Denker <jsd@av8n.com>]

On 07/10/2011 07:35 AM, Aburr@aol.com wrote:
> I have been reading about the laser and magnetic field experiments
> that trap cold atoms for additional experiments. I can understand the
> laser part but  I need a short description of how the magnetic field
> interacts with the neutral  atoms. 

I'm not sure what sort of answer is expected, so let me say a
few things that /might/ be helpful.

 *) The atoms do not have net electrical charge (electric dipole
   moment).  Well, sometimes they do, but then the game is called
   /ion/ trapping, and that's explicitly not what was asked about,
   so let's skip this and move on.
 *) The atoms may have an electric dipole moment, which is important
   because it interacts with the laser, i.e. the optical part of the
   magneto-optical trap (MOT).  Again that's not what was asked about,
   so let's move on.
 *) The atoms do not have any magnetic monopole moment.  Or if they
   do, nobody has noticed it.  :-)
 *) The atoms have a magnetic dipole moment.  You know the sodium
   atom is going to have a whopping big magnetic dipole moment, from
   the spin of the unpaired electron.  It's a little bar magnet.
   Indeed, the entire magnetism of a macroscopic macroscopic bar is
   explained by a bunch of unpaired electrons inside it, all spinning
   the same direction.

   So, at this level of detail, the answer is that the magnetic dipole
   moment interacts with the applied magnetic field.  A gradient in
   the field creates a force on the atom ... as in the famous Stern-
   Gerlach effect.

The laws of physics do not permit a pattern of field gradients that
would create an unconditionally-stable trap.  

The simplest trap that works at all uses a Maxwell pair, aka an anti-Helmholtz
pair.  You know by symmetry that the field will be zero in the middle.  The
magnitude |B| increases in all directions from there.

The next crucial idea is this:  If an atom moves along a field line, if the
field line bends, the spin will precess around the new field-line-direction,
so that the average magnetization follows the field line ... and to first
order the energy of the atom depends only on |B|.  There are lots of things
that could go wrong with this, but it sorta works -- temporarily -- for 
sufficiently cold atoms.

Other field-patterns that are sometimes used are much more complicated.
Here's a review article:
  http://apu.phys.unm.edu/~deutschgroup/Classes/Phys500F03/Downloads/r009r2.pdf
Magnetic trapping is section 5 therein.

And another, with better diagrams:
  http://hexagon.physics.wisc.edu/teaching/2007s_ph449/interesting%20papers/adams%20riis%20laser%20cooling%20review%201977.pdf

If that's not the sort of answer that was wanted, please ask a more
specific question.