Let’s say we have a two-level atom at rest:
If we bombard this atom with a resonant photon which is absorbed,
the atom gets a kick in the direction of the original photon. The
atom acquires momentum:
The corresponding energy is (for a sodium atom with mass number A=23):
To appreciate how small this is, let us convert this energy into
degrees Kelvin. Incidentally, this is called the single-photon
recoil temperature limit (for obvious reasons):
 
So far, we have only considered an absorption event. Now, an
excited atom decays back to the ground state with rate γ0
= 1/τ0 (this is not unlike some students who get
excited about their work for a while, but then inevitably relax to
their normal state). An important point is that the fluorescence
photon emitted in the process of de-excitation goes in a random
direction (actually, sometimes this statement is not completely
true, i.e. there are favored and disfavored emission directions,
e.g. the familiar dipole radiation pattern , but this is not
essential right now). When this happens, atom
recoils in a random direction.
If we keep doing this: absorbing photons from a laser beam and
emitting photons in random directions, we get the atom moving in
the direction of the laser beam, and we also “heat” the motion in
orthogonal directions as a result of “random walk” kicks. What
we’ve said so far is actually already enough to understand how
people slow down and even stop atomic beams. For simplicity, let’s
say we have an atomic beam where all atoms move with the same
velocity vb.
We shine a monochromatic laser beam head-on onto the atoms. We
need to tune the laser
frequency in such a way that the photons are in resonance with the
atomic transition (ω0),
i.e. we need to compensate for the Doppler shift:
From (3) we se that the laser has to be “red-detuned”, i.e. its
frequency has to be
somewhat lower than the atomic resonance frequency
ω0.
OK, so now the atoms happily interact with the photons and slow
down somewhat. At
this point, we have a slight problem since vb has changed and the
resonance condition (3)
is no longer satisfied. If we want to continue slowing a certain
group of atoms, we can
chirp (gradually increase) the laser frequency. Another ingenious
technique of keeping
the atoms on resonance – Zeeman Slowing – is dealt with in the
homework. In this
technique, the atomic beam travels in a changing magnetic field,
so the changing Zeeman
shifts compensate for the slowing effect, keeping the atoms on
resonance with a laser
beam of a fixed frequency. |
