How does the Zeeman Effect contribute to laser cooling of atoms?

[The Head]

I have a couple of questions regarding laser cooling. I should preface this by saying that I've taken a course in Modern Physics, so I don't have more than a very basic understanding of QM. In this case, I am familiar with absorption/emission lines, Zeeman effect, degeneracy and quantum numbers, and the Doppler shift at the elementary level.

1) I am confused about how a magnetic field can precisely be responsible for the continued slowing of atoms. I've read that essentially the decrease in the Doppler shift is compensated for by a decrease in the Zeeman effect. So it seems after initially interacting with the laser, the atom slows down and "sees" a smaller frequency, but as the B-field is weaker, it actually will absorb this lower frequency because the new transition is smaller. But is the Zeeman shift exactly compensate the Doppler shift, so that as the atom moves down the axis the experimenter will not need to change the laser frequency? That these two factors would cancel each other out exactly seems unlikely/remarkable to me. And if that isn't it, what really is the advantage to using the magnetic field?

As a concrete example, would it be fair to say this: An atom is in the ground state, interacts with the laser in a magnetic field, and then may have the energy state defined by n,l,m=1,1,1 (for ex.); it then re-emits the photon in a random direction and goes back to the ground state. As it proceeds through more slowly, it continues to absorb and emit. Is that correct?

2) Are these atoms bouncing back and forth on the walls until they gradually slow down, or will the atoms grind to a (near) halt all in one pass?

3) How exactly is polarization of laser light related to the Zeeman Effect? I am confused as to why this happens.

Thanks for reading and I appreciate any help with this!

 

[mfb]

You always have atoms with different velocity and the laser interacts with a specific velocity (in one direction) only. As you cool your sample, more and more atoms will be below that velocity, and cooling gets inefficient. If you decrease the magnetic field, your laser can interact with slower atoms, and cooling continues.

That these two factors would cancel each other out exactly seems unlikely/remarkable to me.

If you use the same line to produce the laser beam (at zero magnetic field)?

 

[Andy Resnick]

I have a couple of questions regarding laser cooling. <snip>

There are many techniques used to slow down an atomic beam- at least 6- but let's first discuss the two you mention: use of a laser and use of a magnetic field.

Use of (only) a laser is straightforward to understand- the laser frequency is swept upward at a certain rate to compensate for the beam slowing down, using the idea of photon emission to remove momentum from the atom.

Using a spatially varying magnetic field in addition to a laser to slow atoms works as long as the Zeeman shifts are different for the ground and excited state. The idea is that the atomic levels are adjusted by a varying magnetic field as the atoms slow, so the laser does not have to change frequency (IIRC)- the decreasing Doppler shift is compensated by the decreasing Zeeman shift. For a magnetic field B(z) = B0(1-z/z0)^1/2, an atomic beam will be slowed at a constant rate.

Now, it must be noted that slowing a beam is distinct from cooling a beam- cooling requires the velocity distribution decrease in width, as opposed to a decrease in the peak velocity. AFAIK, polarization control of the lasers is more important for cooling below the Doppler limit- there must be a polarization gradient for a laser-only system or a constant (circular) polarization in combination with a magnetic field.

A good source for this material (and more) is Metcalf and van der Straten, "Laser Cooling and Trapping"

 

[The Head]

Thanks very much for your replies, particularly for clearing up polarization. I am still a bit unclear about one thing. It makes sense to me that as the particle moves through the decreasing B field that this will help offset the smaller frequency the particle experiences as it slows. I just want to ensure that the change in frequency the particle experiences is EXACTLY compensated by the smaller Zeeman Effect transition of the electron upon absorbing the laser. That the change in doppler shift due to the particle slowing down always matches the smaller Zeeman effect is what seems too coincidental to me.

 

[Andy Resnick]

It's not coincidental- the magnetic field is designed that way, for a specific atomic species, specific initial conditions, and specific final conditions.