0198506961.pdf

182 Laser cooling and trapping

range of Doppler shifts approximately equal to the homogeneous width

of the transition.^11 Atoms that interact strongly with the laser light slow

(^11) This range is similar to the width of
the hole burnt in the ground-state pop-
ulation in saturated absorption spectro-
scopy. In practice, power broadening
makes the homogeneous width larger
than the natural width.
down until the change in their Doppler shift takes them out of resonance
with the light. This change must be compensated for in order to keep
the force close to its maximum value throughout the slowing process.

9.2 Slowing an atomic beam

The two pioneering laser cooling experiments used different methods to

compensate for the change in Doppler shift as the atoms slowed down.

William Phillips and co-workers used the ingenious method shown in

Fig. 9.2 in which the atomic beam travels along the axis of a tapered

solenoid; the Zeeman effect of the varying magnetic field perturbs the

atomic energy levels so that the transition frequency matches a constant

laser frequency. In the other method the laser frequency was changed

and this so-called chirp cooling is described in the next section. From

eqns 9.7 and 9.8 we see that during constant deceleration the velocity

at distancezfrom the starting point is given by

v=v 0

(

1 −

z

L 0

) 1 / 2

. (9.9)

To compensate for the change in Doppler shift as the atoms slow down

fromv 0 to the chosen final velocity, the frequency shift caused by the

Zeeman effect needs to obey the condition

ω 0 +

μBB(z)

=ω+kv. (9.10)

On the left-hand side, the Zeeman shift for an atomic magnetic moment

μBincreases the atomic resonance frequency fromω 0 , its value at zero

Fig. 9.2The first Zeeman slowing ex-
periment. The solenoid produces a
magnetic field that varies with posi-
tion along the atomic beam so that
the Zeeman shift compensates for the
change in the Doppler shift as atoms
decelerate. A probe laser beam inter-
sects the slow atomic beam at a point
downstream and the laser frequency is
scanned to give a fluorescent signal pro-
portional to the velocity distribution,
similar to that shown in Fig. 9.4 (from
a different experiment). This procedure
records the component of the atomic
velocity along the probe beam and the
angle of intersection mustnotbe 90◦.
(Here we have the opposite requirement
to that in Fig. 8.2.) Adapted from
Phillipset al. (1985).

Na

source

1.1 m

Varying-field

solenoid

Observation

region

Collection

optics

Cooling laser

beam

Probe laser

beam