9.9 An atomic fountain 2110 0(a) (b) (c) (d)21
0 0More atoms
in rangeFig. 9.21One step in the sequence of operations in Raman cooling. (a) Velocity selection by a Raman pulse that transfers
atoms that have velocities within a certain narrow range from| 1 〉to| 2 〉—the process of absorption and stimulated emission
changes the atomic velocity by− 2 vr. (b) Atoms are excited from level 2 to leveliby another laser beam—in this process the
atomic velocity changes byvr. (c) Atoms decay to level 1 by spontaneous emission—the recoil in a random direction means
that the atoms return to level 1 with a component of velocity anywhere in the rangevtov− 2 vr,wherevis the initial velocity.
There are more atoms in the narrow velocity class aroundv= 0 than at the start of the sequence. (d) Repetition of the
sequence with different initial velocities increases the number of atoms withv 0 until they are ‘piled’ up in a distribution
whose width is much less than the recoil velocityvr.
The time taken for atoms to fall (randomly) into a velocity class of
width 2δvincreases asδvdecreases and this determines the final velocity
spread achievable by Raman cooling in practice.
Raman cooling works well in one dimension, but it is much less effi-
cient in three dimensions where the target is to have all three components
vx,vyandvzbetween±δv. Another method of sub-recoil cooling called
velocity-selective coherent population trapping is also a stochastic pro-
cess, see Metcalf and van der Straten (1999) and Bardouet al. (1991).
Raman transitions are also used for matter-wave interferometry based
on ultra-cold atoms (Chapter 10).
9.9 An atomic fountain
The slow atoms produced by laser cooling have led to a dramatic im-
provement in measurements whose resolution is limited by the interac-
tion time. Cold atoms can be confined in dipole-force traps^74 for long
(^74) Or magnetic traps as described in the
next chapter.