Can the volume of a Magnetoptical Trap be estimated from a 2D projection?

[ChrisVer]

Hi,

I was just wondering, is there any way to estimate the vollume of a MOT (formed by 3 incoming and 3 counterpropating beams at a point where the magnetic field B=0) just by seeing its 2D projection (maybe through a camera) ?
I could only measure its 2 dimensions in the picture:

h=0.9 mm
d=0.6 mm

However is there anyway to determine the 3D dimensional overlapping of the 3 propagating laser beams?
Naturally if everything is perfect I think I can have a sphere... now obviously the image is not a sphere but an ellipse... I thought I could try to say that the extra dimension x=0.6 (oblate spheroid) to 0.9 (prolate spheroid) mm, but I think this doesn't make sense... It can as well be anything from 0.1 mm (even smaller) to 2*Radius[laser] ... right?

 

[DrClaude]

Don't forget the "M" in MOT: the trap is not defined only by the laser beams, but also by the magnetic field. There is no reason to assume it is it will follow the simply from the size of the laser beam. I think you need to also image the atoms along the other axis to get the full size. (Caveat: I'm not an experimentalist, so there might be tricks using atom number or density to recover the full size.)

Also, I would not call that the volume of the MOT, but rather the volume of the cloud of trapped atoms. The size will of course depend very much on the temperature of the atoms in the MOT.

 

[ChrisVer]

isn't it legit to assume that the center of the magnetic field coincides with the center of the 2D disk?
I'm not really sure (I'm not an experimentalist either, just trying to make a plausible assumption), but that's how I imagine it.
Eg. If I look at a spheroid I'm looking at some 2D projection of it (in my eyes-not in a camera), however I have a feeling that although I don't see its 3rd dimension coinciding with my line of view, I am seeing the center of the spheroid in the center of the disk... is that wrong?

The size of the 3rd dimension will eventually depend on the overlapping of the 3rd beam with the rest beams (creating the 2D disk) around that center's position, that's why I'm thinking it can be either equal to the total size of the laser beam or 0 (of course not exactly zero but some threshold distance, it can't be zero because otherwise the MOT wouldn't be created).

 

[DrClaude]

isn't it legit to assume that the center of the magnetic field coincides with the center of the 2D disk?

Strictly speaking, this is only the case if the alignment is perfect. Experimentally, this is not an easy task, as you have to get 6 laser beams to meet at the center of a magnetic field.

That said, I don't know what you want to achieve, so you it might well be that you can ignore any misalignment and assume a perfect setup.

I'm not really sure (I'm not an experimentalist either, just trying to make a plausible assumption), but that's how I imagine it.
Eg. If I look at a spheroid I'm looking at some 2D projection of it (in my eyes-not in a camera), however I have a feeling that although I don't see its 3rd dimension coinciding with my line of view, I am seeing the center of the spheroid in the center of the disk... is that wrong?

It depends on where the camera is placed. Is it in the plane of four of the beams?

The size of the 3rd dimension will eventually depend on the overlapping of the 3rd beam with the rest beams (creating the 2D disk) around that center's position, that's why I'm thinking it can be either equal to the total size of the laser beam or 0 (of course not exactly zero but some threshold distance, it can't be zero because otherwise the MOT wouldn't be created).

What do you mean by "total size of the laser beam". The beams have most probably a Gaussian profile. And the shape of the cloud will depend on the magnetic field also, which is different in one direction than in the two others (assuming it is produced by two coils in an anti-Helmholtz configuration).