M1L2i.txt

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With rapid adiabatic passage I've
discussed with you the physics that rapid precession
keeps a magnetic moment aligned with an effective magnetic
field.
Let me now discuss the same phenomenon,
but in a very different environment.
And this is a similar process happening in a magnetic trap.
In a magnetic trap, we don't have any drive,
or we have a time dependent field.
But what happens is we have a magnetic field,
but the atoms move through the atom trap.
So the atom sees a changing magnetic field.
And in many of our experiments here at MIT,
we use a quadrupolar field.
We've discussed some of these aspects in 8.422.
So a quadrupolar field, the field
has to be inhomogenous in order to provide trapping forces.
So we often use quadrupolar fields.
They have a lot of advantages.
That's how we build the tightest magnetic traps.
But what happens now is if an atom
moves along this trajectory from the-- it
moves up in the laboratory, here let's
say the atom is in spin up.
Here it's now aligned.

The magnetic field is opposite to the spin,
and now it moves up, and now the magnetic field up here
is pointing up.
The physics I explained to you, rapid adiabatic passage
means that the rapid precession of the spin
means that as the atom moves, the spin stays aligned
with the magnetic field.
So you find the same physics here
in a different environment, but the mathematical description
is the same.

Of course, and that's my last comment for today,
if you have a spherical quadrupolar trap,
and you go right through the origin, you're out of luck.
Because here the atom sees the magnetic field is down,
it gets smaller.
The magnetic field gets smaller, gets smaller.
The magnetic field gets zero.
Oopsie.
The magnetic field points in the other direction.
And there was no warning.
The magnetic field has jumped from 0 degrees to 180 degrees.
There was never, ever any transverse field
around which the atom could precess and change
its orientation.
So therefore when an atom is aligned
with the magnetic field moves through the origin-- oopsie,
it's anti-aligned.
It has lost its orientation with respect to the magnetic field,
and this is the breakdown of rapid adiabatic passage,
because there's no adiabaticity.
It is not an adiabatic change of the direction
of the magnetic field, it's a sudden field.
And the consequences are bad.
You lose your atoms from the magnetic trap.
It's called Majorana losses.
And a lot of people know what I'm talking about,
but I'm not explaining it in detail.
Time is over.
Any questions about what I've discussed?
Yes?
I would say the question is about the frequency width,
and if you switch on the frequency drive,
it's not a delta function.
If you are far away from resonance,
it doesn't really matter.
There is, of course, a criterion that the width,
the effective width of the frequency
should not be comparable to the detuning.
So then you switch it on, but you're so far away
from resonance that it doesn't matter
if you have a small width.
The effective detuning is still large.
You scan through resonance.
But these are sort of the boundary conditions.
The exact solution of the Landau-Zener problem,
for instance, assumes you go from minus infinity
to plus infinity in the detuning.
Nobody does that.
So we're discussing sort of finite -- sweep finite duration
effects, but usually we can be pretty
close to the idealized assumption.